Search results for: Kolmogorov-Chentsov continuity theorem

Authors: T. J. Stepien, L. T. Stepien

Abstract:

This abstract concerns an extremely fundamental issue. Namely, the fundamental problem of science is the issue of consistency. In this abstract, we present the theorem saying that the classical calculus of quantifiers is inconsistent in the traditional sense. At the beginning, we introduce a notation, and later we remind the definition of the consistency in the traditional sense. S1 is the set of all well-formed formulas in the calculus of quantifiers. RS1 denotes the set of all rules over the set S1. Cn(R, X) is the set of all formulas standardly provable from X by rules R, where R is a subset of RS1, and X is a subset of S1. The couple < R,X > is called a system, whenever R is a subset of RS1, and X is a subset of S1. Definition: The system < R,X > is consistent in the traditional sense if there does not exist any formula from the set S1, such that this formula and its negation are provable from X, by using rules from R. Finally, < R0+, L2 > denotes the classical calculus of quantifiers, where R0+ consists of Modus Ponens and the generalization rule. L2 is the set of all formulas valid in the classical calculus of quantifiers. The Main Result: The system < R0+, L2 > is inconsistent in the traditional sense.

Keywords: classical calculus of quantifiers, classical predicate calculus, generalization rule, consistency in the traditional sense, Modus Ponens

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Authors: Tarul Garg, P. N. Agrawal

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We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

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Authors: Amar Partap Singh Pharwaha, Balkrishan Jindal

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In this paper, a new method is developed for hiding image in a digital image with multilayer security. In the proposed method, the secret image is encrypted in the first instance using a flexible matrix based symmetric key to add first layer of security. Then another layer of security is added to the secret data by encrypting the ciphered data using Pythagorean Theorem method. The ciphered data bits (4 bits) produced after double encryption are then embedded within digital image in the spatial domain using Least Significant Bits (LSBs) substitution. To improve the image quality of the stego-image, an improved form of pixel adjustment process is proposed. To evaluate the effectiveness of the proposed method, image quality metrics including Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), entropy, correlation, mean value and Universal Image Quality Index (UIQI) are measured. It has been found experimentally that the proposed method provides higher security as well as robustness. In fact, the results of this study are quite promising.

Keywords: Pythagorean theorem, pixel adjustment, ciphered data, image hiding, least significant bit, flexible matrix

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Authors: Urbánek Jiří J., Krahulec Josef, Urbánek Jiří F., Johanidesová Jitka

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These Computational assistance for the research and modelling of critical infrastructure subjects continuity deal with this paper. It enables us the using of prevailing operation system MS Office (SmartArt...) for mathematical models, using DYVELOP (Dynamic Vector Logistics of Processes) method. It serves for crisis situations investigation and modelling within the organizations of critical infrastructure. In the first part of the paper, it will be introduced entities, operators and actors of DYVELOP method. It uses just three operators of Boolean algebra and four types of the entities: the Environments, the Process Systems, the Cases and the Controlling. The Process Systems (PrS) have five “brothers”: Management PrS, Transformation PrS, Logistic PrS, Event PrS and Operation PrS. The Cases have three “sisters”: Process Cell Case, Use Case and Activity Case. They all need for the controlling of their functions special Ctrl actors, except ENV – it can do without Ctrl. Model´s maps are named the Blazons and they are able mathematically - graphically express the relationships among entities, actors and processes. In the second part of this paper, the rich blazons of DYVELOP method will be used for the discovering and modelling of the cycling cases and their phases. The blazons need live PowerPoint presentation for better comprehension of this paper mission. The crisis management of energetic crisis infrastructure organization is obliged to use the cycles for successful coping of crisis situations. Several times cycling of these cases is a necessary condition for the encompassment of the both the emergency event and the mitigation of organization´s damages. Uninterrupted and continuous cycling process bring for crisis management fruitfulness and it is a good indicator and controlling actor of organizational continuity and its sustainable development advanced possibilities. The research reliable rules are derived for the safety and reliable continuity of energetic critical infrastructure organization in the crisis situation.

Keywords: blazons, computational assistance, DYVELOP method, critical infrastructure

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Authors: Afy Syahidan ACHMAD, Astin NURDIANA, SURYANTINI

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In volcanic arc environment we can find multiple volcanic deposits which overlapped with another volcanic deposit so it will complicates source and distribution determination. This problem getting more difficult when we can not trace any deposit border evidences in field especially in high vegetation volcanic area, or overlapped deposit with same characteristics. Main purpose of this study is to solve complex volcanostratigraphy mapping problems trough ridge, valley, and river continuity. This method application carried out in Old Sunda Volcanic, West Java, Indonesia. Using 1:100.000 and 1:50.000 topographic map, and regional geology map, old sunda volcanic deposit was differentiated in regional level and detail level. Final product of this method is volcanostratigraphy unit determination in reconnaissance stage to simplify mapping process.

Keywords: volcanostratigraphy, study, method, volcanic deposit

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Authors: Nazish Iftikhar, Adil Jhangeer, Tayyaba Naz

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The universe is expanding at an accelerated rate. Symmetries are useful in understanding universe’s behavior. Emmy Noether reported the relation between symmetries and conservation laws. These symmetries are known as Noether symmetries which correspond to a conserved quantity. In differential equations, conservation laws play an important role. Noether symmetries are helpful in modified theories of gravity. Time independent plane symmetric spacetime was classified by Noether`s theorem. By using Noether`s theorem, set of linear partial differential equations was obtained having A(r), B(r) and F(r) as unknown radial functions. The Lagrangian corresponding to considered spacetime in the Noether equation was used to get Noether operators. Different possibilities of radial functions were considered. Firstly, all functions were same. All the functions were considered as non-zero constant, linear, reciprocal and exponential respectively. Secondly, two functions were proportional to each other keeping third function different. Second case has four subcases in which four different relationships between A(r), B(r) and F(r) were discussed. In all cases, we obtained nontrivial Noether operators including gauge term. Conserved quantities for each Noether operators were also presented.

Keywords: Noether gauge symmetries, radial function, Noether operator, conserved quantities

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Authors: A. U. Haque, W. Asrar, A. A Omar, E. Sulaeman, J. S. M. Ali

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Buoyancy force applied on deformable symmetric bodies can be estimated by using Archimedes Principle. Such bodies like ellipsoidal bodies have high volume to surface ratio and are isometrically scaled for mass, length, area and volume to follow square cube law. For scaling up such bodies, it is worthwhile to find out the scaling relationship between the other physical quantities that represent thermodynamic, structural and inertial response etc. So, dimensionless similarities to find an allometric scale can be developed by using Bukingham π theorem which utilizes physical dimensions of important parameters. Base on this fact, physical dependencies of buoyancy system are reviewed to find the set of physical variables for deformable bodies of revolution filled with expandable gas like helium. Due to change in atmospheric conditions, this gas changes its volume and this change can effect the stability of elongated bodies on the ground as well as in te air. Special emphasis was given on the existing similarity parameters which can be used in the design of experiments of such bodies whose shape is affected by the external force like a drag, surface tension and kinetic loads acting on the surface. All these similarity criteria are based on non-dimensionalization, which also needs to be consider for scaling up such bodies.

Keywords: Bukhigham pi theorem, similitude, scaling, buoyancy

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Authors: Mirza Adil Ahmad Mughal

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Transcendental analytics, in the critique of pure reason, combines space and time as conditions of the possibility of the phenomenon from the transcendental aesthetic with the pure magnitude-intuition notion. The property of continuity as a qualitative result of the additive magnitude brings the possibility of connecting with experience, even though only as a potential because of the a priori necessity from assumption, as syntheticity of the a priori task of a scientific method of philosophy given by Kant, which precludes the application of categories to something not empirically reducible to the content of such a category's corresponding and possible object. This continuity as the qualitative result of a priori constructed notion of magnitude lies as a fundamental assumption and property of, what in Microeconomic theory is called as, 'choice rules' which combine the potentially-empirical and practical budget-price pairs with preference relations. This latter result is the purest qualitative side of the choice rules', otherwise autonomously, quantitative nature. The theoretical, barring the empirical, nature of this qualitative result is a synthetic a priori truth, which, if at all, it should be, if the axiomatic structure of the economic theory is held to be correct. It has a potentially verifiable content as its possible object in the form of quantitative price-budget pairs. Yet, the object that serves the respective Kantian category is qualitative itself, which is utility. This article explores the validity of Kantian qualifications for this application of 'categories' to the economic structure of society.

Keywords: categories of understanding, continuity, convexity, psyche, revealed preferences, synthetic a priori

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Authors: Farid Adisaputra Gumilang

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Kucing Liar Underground Mine is a future mine of PT Freeport Indonesia PTFI that is currently being developed. In the development process, problems were found when blasting the tunnels; there were overbreak, and void occur caused by geological contact or poor rock conditions. Geotechnical engineers must evaluate not only the remnant capacity of ground support systems but also investigate the depth of rock mass yield within pillars. To prevent the potential hazard caused by void zones, geotechnical engineers must ensure the planned drift is mined in the best location where people can work safely. GPR, or Ground penetrating radar, is a geophysical method that can image the subsurface. This non-destructive method uses electromagnetic radiation and detects the reflected signals from subsurface structures. The GPR survey measurements are conducted 48 meters along the drift that has a poor ground condition with 150MHz antenna with several angles (roof, wall, and floor). Concern grounds are determined by the continuity of reflector/low reflector in the radargram section. Concern grounds are determined by the continuity of reflector/low reflector in the radargram section. In this paper, processing data using instantaneous amplitude to identify the void zone. In order to have a good interpretation and result, it combines with the geological information and borehole camera data, so the calibrated GPR data allows the geotechnical engineer to determine the safe location to change the drift location.

Keywords: underground mine, ground penetrating radar, reflectivity, borehole camera

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Authors: Satya Deo, Deepak Kumar Maurya

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The present study investigates the ow of a Newtonian fluid sandwiched between two rectangular porous channels filled with micropolar fluid in the presence of a uniform magnetic field applied in a direction perpendicular to that of the fluid motion. The governing equations of micropolar fluid are modified by Nowacki's approach. For respective porous channels, expressions for velocity vectors, microrotations, stresses (shear and couple) are obtained analytically. Continuity of velocities, continuities of micro rotations and continuity of stresses are used at the porous interfaces; conditions of no-slip and no spin are applied at the impervious boundaries of the composite channel. Numerical values of flow rate, wall shear stresses and couple stresses at the porous interfaces are calculated for different values of various parameters. Graphs of the ow rate and fluid velocity are plotted and their behaviors are discussed.

Keywords: couple stress, flow rate, Hartmann number, micropolar fluids

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Authors: Manoj K. Kumar, Deepthi Bathala

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Man has the need to know and feel as a part of the historical continuum and it is this continuum that reinforces his identity. Architecture and the built environment contribute to this identity as established by the various identity theories exploring the relationship between the two. Architecture which is organic has been successful in maintaining a continuum of identity until the advent of globalization when the world saw a drastic shift to architecture of ‘placelessness’. The answer to the perfect synthesis of ‘universalization’ and ‘regionalism’ is an ongoing quest. However, history has established a smooth transition from vernacular to colonial to modern unlike the architecture of today. The traditional Kerala architecture has evolved from the tropical climate, geography, local needs, materials, skills and foreign influences. It is unique in contrast to the architecture of the neighboring states as a result of the geographical barriers however influenced by the architecture of the Orient due to trade relations. Through 1805 to 1950, the European influence on the architecture of Kerala resulted in the emergence of the colonial style which managed to establish a continuum of the traditional architecture. The paper focuses on the identification of the components of architecture that established the continuity of place-identity in the architecture of Kerala and examines the transition from the traditional Kerala architecture to colonial architecture during the colonial period. Visual surveys based on the principles of urban design, cognitive mapping, typology analysis followed by the strong understanding of the morphological and built environment along with the matrix method are the research tools used. The understanding of these components of continuity can be useful in creating buildings which people can relate to in the present day. South-Asia shares the history of colonialism and the understanding of these components can pave the way for further research on how to establish a regional identity in the era of globalization.

Keywords: colonial, identity, place, regional

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Authors: Yuyang Cheng, Marcos Escobar-Anel

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This paper introduces a multivariate 4/2 stochastic covariance process generalizing the one-dimensional counterparts presented in Grasselli (2017). Our construction permits stochastic correlation not only among stocks but also among volatilities, also known as co-volatility movements, both driven by more convenient 4/2 stochastic structures. The parametrization is flexible enough to separate these types of correlation, permitting their individual study. Conditions for proper changes of measure and closed-form characteristic functions under risk-neutral and historical measures are provided, allowing for applications of the model to risk management and derivative pricing. We apply the model to an expected utility theory problem in incomplete markets. Our analysis leads to closed-form solutions for the optimal allocation and value function. Conditions are provided for well-defined solutions together with a verification theorem. Our numerical analysis highlights and separates the impact of key statistics on equity portfolio decisions, in particular, volatility, correlation, and co-volatility movements, with the latter being the least important in an incomplete market.

Keywords: stochastic covariance process, 4/2 stochastic volatility model, stochastic co-volatility movements, characteristic function, expected utility theory, verication theorem

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Authors: Damir Latypov

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A closed-form solution for 4-D double surface integrals arising in boundary integrals equations of a potential theory is obtained for arbitrary coplanar polygonal surfaces. The solution method is based on the construction of exact differential forms followed by the application of Stokes' theorem for each surface integral. As a result, the 4-D double surface integral is reduced to a 2-D double line integral. By an appropriate change of variables, the integrand is transformed into a separable function of integration variables. The closed-form solutions to the corresponding 1-D integrals are readily available in the integration tables. Previously closed-form solutions were known only for the case of coincident triangle surfaces and coplanar rectangles. Solutions for these cases were obtained by surface-specific ad-hoc methods, while the present method is general. The method also works for non-polygonal surfaces. As an example, we compute in closed form the 4-D integral for the case of coincident surfaces in the shape of a circular disk. For an arbitrarily shaped surface, the proposed method provides an efficient quadrature rule. Extensions of the method for non-coplanar surfaces and other than 1/R integral kernels are also discussed.

Keywords: boundary integral equations, differential forms, integration, stokes' theorem

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Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

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In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming

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Authors: Marwa Sahnoun, Chokri Abdennadher

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This article comes, very timely, to look at the effectiveness of active labor market policies (ALMP) in improving labor market outcomes. Using panel data estimates for 19 European countries during the period 2000-2012, this article showed the role of institutional factors, especially the role of employment policies implementation based on three variables: the allocation of resources for the implementation of policies, continuity and timing in the implementation of policies to capture their effectiveness on the labor market. Empirical results shows favor effect of training, employment incentives, sheltered employment and rehabilitation and direct job creation on the entire population employment growth. Results shows also that start-up incentives seems to be more effective in increasing employment than other types of policies. Importantly, two aspects are important in terms of implementation: public expenditure on program administration, e.g. (PES) watches the most favorable aspect and the continuity of policies implemented.

Keywords: active labor market policies, implementation, public expenditure on program administration, start-up incentives, training

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Authors: Hashem Sazegar

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Legendre’s conjecture states that there is a prime number between n^2 and (n + 1)^2 for every positive integer n. In this paper we prove that every composite number between n2 and (n + 1)2 can be written u^2 − v^2 or u^2 − v^2 + u − v that u > 0 and v ≥ 0. Using these result as well as induction and residues (modq) we prove Legendre’s conjecture.

Keywords: bertrand-chebyshev theorem, landau’s problems, goldbach’s conjecture, twin prime, ramanujan proof

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Authors: Naomi Huang Wenya, Xin Xiaohui, Vijaya Rao, Wong Ting Hway, Chow Kah Hoe Pierce, Tan Hiang Khoon

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Background: The majority of the cancelled elective surgeries caused by the COVID-19 pandemic globally were estimated to occur in low- and middle-income countries (LMICs), where surgical services had long been in short supply even before the pandemic. Therefore, minimising disruption to existing surgical care in LMICs is of crucial importance during a pandemic. This study aimed to explore contributory factors to the continuity of surgical care in LMICs, in the face of a pandemic. Methods: Semi-structured interviews were conducted over zoom, with surgical leaders of 25 tertiary hospitals from 11 LMICs in South and Southeast Asia, from September to October 2020. Key themes were subsequently identified from the interview transcripts, using Braun and Clarke's method of thematic analysis. Results: The COVID-19 pandemic affected all surgical services of participating institutions but to varying degrees. Overall, elective surgeries suffered the gravest disruption, followed by outpatient surgical care, and finally, emergency surgeries. Keeping healthcare workers safe and striving for continuity of essential surgical care emerged as notable response strategies observed across all participating institutions. Conclusion: This study suggested that four factors are important for the resilience of surgical care against COVID-19: adequate COVID-19 testing capacity and effective institutional infection control measures, designated COVID-19 treatment facilities, a whole-system approach to balancing pandemic response and meeting essential surgical needs, and active community engagement. These findings can inform healthcare institutions in other countries, especially LMICs, in their effort to tread a fine line between preserving healthcare capacity for pandemic response and protecting surgical services against pandemic disruption.

Keywords: COVID-19, pandemic, LMICs, continuity of surgical service

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Authors: Asal Pournaghshband

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This paper presents the development of a finite element model to study the large deflection behavior of restrained stainless steel cellular beams at elevated temperature. Cellular beams are widely used for efficient utilization of raw materials to facilitate long spans with faster construction resulting sustainable design solution that can enhance the performance and merit of any construction project. However, their load carrying capacity is less than the equivalent beams without opening due to developing shear-moment interaction at the openings. In structural frames due to elements continuity, such beams are restrained by their adjoining members which has a substantial effect on beams behavior in fire. Stainless steel has also become integral part of the build environment due to its excellent corrosion resistance, whole life-cycle costs, and sustainability. This paper reports the numerical investigations into the effect of structural continuity on the thermo-mechanical performance of restrained steel beams with circle and elongated circle shapes of web opening in fire. The numerical model is firstly validated using existing numerical results from the literature, and then employed to perform a parametric study. The structural continuity is evaluated through the application of different levels of axial restraints on the response of carbon steel and stainless steel cellular beam in fire. The transit temperature for stainless steel cellular beam is shown to be less affected by the level of axial stiffness than the equivalent carbon steel cellular beam. Overall, it was established that whereas stainless steel cellular beams show similar stages of behavior of carbon steel cellular beams in fire, they are capable of withstanding higher temperatures prior to the onset of catenary action in large deflection, despite the higher thermal expansion of stainless steel material.

Keywords: axial restraint, catenary action, cellular beam, fire, numerical modeling, stainless steel, transit temperature

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Authors: Yvonne Ayerki Lamptey

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The expanding informal sector in developing countries and in Ghana in particular from the 1980s has now been aggravated by the growing population and downsizing in both the public and private sectors, with displaced workers finding alternative livelihoods in the informal sector. Youth and graduate unemployment also swell the numbers and further promote the continuity of the sector. Formal workers and institutions facilitate the growth and complicate demarcations between informality within the formal and informal sectors. In spite of its growth and increasing importance, the informal economy does not feature in policy debates and has often been neglected by the Ghana government. The phenomenon has evolved with modernity into myriad unimaginable forms. Indeed, actors within the sector often clash with the interventions provided by policy makers - because neither the operatives nor the activities they perform can be clearly defined. This study uses in-depth interviews to explore the behavioural nature of the informal workers in Ghana to understand how the operatives describe and perceive the sector, and to identify the factors that influence their drive to stay within the sector. This paper concludes that the operatives clearly distinguish between the formal and informal sectors and identify the characteristics and conditions that constitute the informal sector. Other workers are trapped between formality and informality. The findings also enumerate the push and pull factors contributing to the growth of the sector.

Keywords: informal employment, informal sector, informal work, informality

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Authors: Melike Aydoğan, Dürdane Öztürk

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Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1).

Keywords: starlike log-harmonic functions, univalent functions, distortion theorem

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Authors: Nazneen Khan, Vakeel A. Khan

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In this article we introduce the Paranorm Zweier I-convergent sequence spaces, for a sequence of positive real numbers. We study some topological properties, prove the decomposition theorem and study some inclusion relations on these spaces.

Keywords: ideal, filter, I-convergence, I-nullity, paranorm

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Authors: Ganiyat Soliu, Glen Bright, Chiemela Onunka

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Performance optimization plays a key role in controlling the waiting time during manufacturing in an advanced manufacturing environment to improve productivity. Queuing mathematical modeling theory was used to examine the performance of the multi-stage production line. Robotics as a disruptive technology was implemented into a virtual manufacturing scenario during the packaging process to study the effect of waiting time on productivity. The queuing mathematical model was used to determine the optimum service rate required by robots during the packaging stage of manufacturing to yield an optimum production cost. Different rates of production were assumed in a virtual manufacturing environment, cost of packaging was estimated with optimum production cost. An equation was generated using queuing mathematical modeling theory and the theorem adopted for analysis of the scenario is the Newton Raphson theorem. Queuing theory presented here provides an adequate analysis of the number of robots required to regulate waiting time in order to increase the number of output. Arrival rate of the product was fast which shows that queuing mathematical model was effective in minimizing service cost and the waiting time during manufacturing. At a reduced waiting time, there was an improvement in the number of products obtained per hour. The overall productivity was improved based on the assumptions used in the queuing modeling theory implemented in the virtual manufacturing scenario.

Keywords: performance optimization, productivity, queuing theory, robotics

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Edoghogho Ogbeifun, Charles Mbohwa, J. H. C. Pretorius

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Effective infrastructure development scheme planned and executed has positive influence on the quantity of available stock of infrastructure to meet the immediate and expansion needs of an organization, as well as contribute to the overall economic development of a nation, community or the local entity where the infrastructure is hosted. It is noteworthy, however, that infrastructure development scheme spans a long time frame, usually longer than the political life of the administration that initiates the scheme. In the majority of circumstances, execution may start and achieve different levels of completion; at best, only limited numbers are completed and put into functional use during the life of the administration that initiated the infrastructure scheme. When there is a change in leadership, many of the uncompleted projects are usually abandoned. The new administration repeats the circle of its predecessors and develops another set of infrastructure scheme which will suffer similar fate as the ones developed by their predecessors; thus doting the landscape with many uncompleted projects, which leads to infrastructure deficit. These circle will continue unless each succeeding leader sees governance as single continuum. Therefore, infrastructure projects not completed by one administration should be continued by succeeding administration, in order to increase the stock of relevant infrastructure available for the smooth operations organization and enhance the needed developments, as well as reduce the negative effects of infrastructure deficit. The single case study of qualitative research method was adopted to investigate the actions of the administration of three successive Vice-Chancellors, in a higher education institution in Nigeria, over a longitudinal period of twelve years. This is with a view to exploring the effects of each administration on the development and execution of infrastructure projects, with particular interest on abandoned projects. The findings revealed that although two of Vice-Chancellors were committed to infrastructure upgrade, they executed more new projects than completing abandoned ones, while the current leader has shown more pragmatism in completing abandoned projects alongside constructing new ones; thus demonstrating the importance of the continuity of governance. In this regard, there is a steady increase in the stock of infrastructure to accommodate the expansion of existing academic programmes, host new ones as well as reduce the negative effects of infrastructure deficit caused by abandoned projects.

Keywords: abandoned projects, continuity of governance, infrastructure development scheme, long time frame

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Authors: Jorge Gonzalez-Camus

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In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Remus Titiriga

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The paper focuses on Pascal's indivisibles evolving to Leibniz's infinitesimals. It starts with parallel developments by the two savants in Combinatorics (triangular numbers for Pascal and harmonic triangles for Leibniz) and their implication in determining the sum of mathematical series. It follows with a focus on the geometrical contributions of Pascal. He considered the cycloid and other mechanical curves the epitome of geometric comprehensibility in a series of challenging problems he posed to the mathematical world. Pascal provided the solutions in 1658, in a volume published under the pseudonym of Dettonville, using indivisibles and ratios between curved and straight lines. In the third part, the research follows the impact of this volume on Leibniz as the initial impetus for the elaboration of modern calculus as an algorithmic method disjoint of geometrical intuition. Then paper analyses the further steps and proves that Leibniz's developments relate to his philosophical frame (the search for a characteristic Universalis, the consideration of principle of continuity or the rule of sufficient reason) different from Pascal's and impacting mathematical problems and their solutions. At this stage in Leibniz's evolution, the infinitesimals replaced the indivisibles proper. The last part of the paper starts with speculation around "What if?". Could Pascal, if he lived more, accomplish the same feat? The document uses Pascal's reconstructed philosophical frame to formulate a positive answer. It also proposes to teach calculus with indivisibles and infinitesimals mimicking Pascal and Leibniz's achievements.

Keywords: indivisibles, infinitesimals, characteristic triangle, the principle of continuity

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Authors: Shin-Shin Kao, Yuan-Kang Shih, Hsun Su

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In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: complement, degree sum, hamiltonian, tough

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Authors: Ellen Van Den Oord, Julien Marie Jan Ferdinand Van Campen

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This article introduces a computationally efficient method for stacking sequence blending of composite structures. The computational efficiency makes the presented method especially interesting for composite structures with a large number of design regions. Optimization of composite structures with an unequal load distribution may lead to locally optimized thicknesses and ply orientations that are incompatible with one another. Blending constraints can be enforced to achieve structural continuity. In literature, many methods can be found to implement structural continuity by means of stacking sequence blending in one way or another. The complexity of the problem makes the blending of a structure with a large number of adjacent design regions, and thus stacking sequences, prohibitive. In this work the local stacking sequence optimization is preconditioned using a method found in the literature that couples the mechanical behavior of the laminate, in the form of lamination parameters, to blending constraints, yielding near-optimal easy-to-blend designs. The preconditioned design is then fed to the scheme using cellular automata that have been developed by the authors. The method is applied to the benchmark 18-panel horseshoe blending problem to demonstrate its performance. The computational efficiency of the proposed method makes it especially suited for composite structures with a large number of design regions.

Keywords: composite, blending, optimization, lamination parameters

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Authors: Zekang Lan, Yan Xu, Yingkun Huang, Dian Huang, Shengzhong Feng

Abstract:

Jobs on high-performance computing (HPC) clusters can suffer significant performance degradation due to inter-job network interference. Topology-aware job allocation problem (TJAP) is such a problem that decides how to dedicate nodes to specific applications to mitigate inter-job network interference. In this paper, we study the window-based TJAP on a fat-tree network aiming at minimizing the cost of communication hop, a defined inter-job interference metric. The window-based approach for scheduling repeats periodically, taking the jobs in the queue and solving an assignment problem that maps jobs to the available nodes. Two special allocation strategies are considered, i.e., static continuity assignment strategy (SCAS) and dynamic continuity assignment strategy (DCAS). For the SCAS, a 0-1 integer programming is developed. For the DCAS, an approach called neural simulated algorithm (NSA), which is an extension to simulated algorithm (SA) that learns a repair operator and employs them in a guided heuristic search, is proposed. The efficacy of NSA is demonstrated with a computational study against SA and SCIP. The results of numerical experiments indicate that both the model and algorithm proposed in this paper are effective.

Keywords: high-performance computing, job allocation, neural simulated annealing, topology-aware

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Authors: Saeed Poormoaied

Abstract:

Perishability and developing an intelligent control policy for perishable items are the major concerns of marketing managers in a supply chain. In this study, we address a two-echelon supply chain problem for perishable items with a single vendor and a single buyer. The buyer adopts an aged-based continuous review policy which works by taking both the stock level and the aging process of items into account. The vendor works under the warehouse framework, where its lot size is determined with respect to the batch size of the buyer. The model holds for a positive and fixed lead time for the buyer, and zero lead time for the vendor. The demand follows a Poisson process and any unmet demand is lost. We provide exact analytic expressions for the operational characteristics of the system by using the renewal reward theorem. Items have a fixed lifetime after which they become unusable and are disposed of from the buyer's system. The age of items starts when they are unpacked and ready for the consumption at the buyer. When items are held by the vendor, there is no aging process which results in no perishing at the vendor's site. The model is developed under the centralized framework, which takes the expected profit of both vendor and buyer into consideration. The goal is to determine the optimal policy parameters under the service level constraint at the retailer's site. A sensitivity analysis is performed to investigate the effect of the key input parameters on the expected profit and order quantity in the supply chain. The efficiency of the proposed age-based policy is also evaluated through a numerical study. Our results show that when the unit perishing cost is negligible, a significant cost saving is achieved.

Keywords: two-echelon supply chain, perishable items, age-based policy, renewal reward theorem

Procedia PDF Downloads 110