Search results for: convexity

Authors: Jatinderdeep Kaur

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In this paper, the results of Kano from one-dimensional cosine and sine series are extended to two-dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as the class of semi convexity and class R are extended from one dimension to two dimensions. Under these extended classes, I have checked the function f(x,y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function. Further, some results are obtained which are the generalization of Moricz's results.

Keywords: conjugate dirichlet kernel, conjugate fejer kernel, fourier series, semi-convexity

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Authors: Ladznar S. Laja, Rosalio G. Artes, Jr.

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This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established.

Keywords: convex subgraph, convex index, generating function, polynomial ring

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Authors: Shashi Kant Mishra

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In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPEC). We establish necessary and sufficient optimality conditions for the SIMPEC, using convexificators. We study the Wolfe type dual problem for the SIMPEC under the ∂∗convexity assumptions. A Mond-Weir type dual problem is also formulated and studied for the SIMPEC under the ∂∗-convexity, ∂∗-pseudoconvexity and ∂∗quasiconvexity assumptions. Weak duality theorems are established to relate the SIMPEC and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification (GS-ACQ).

Keywords: mathematical programming problems with equilibrium constraints, optimality conditions, semi-infinite programming, convexificators

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Authors: Choki, Supatchai Boonpratham, Suwannee Luppanapornlarp

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The objective of this study was to find a correlation between cephalometric measurements and visual perception of facial profile in skeletal type II patients. In this study, 250 lateral cephalograms of female patients from age, 20 to 22 years were analyzed. The profile outlines of all the samples were hand traced and transformed into silhouettes by the principal investigator. Profile ratings were done by 9 orthodontists on Visual Analogue Scale from score one to ten (increasing level of convexity). 37 hard issue and soft tissue cephalometric measurements were analyzed by the principal investigator. All the measurements were repeated after 2 weeks interval for error assessment. At last, the rankings of visual perceptions were correlated with cephalometric measurements using Spearman correlation coefficient (P < 0.05). The results show that the increase in facial convexity was correlated with higher values of ANB (A point, nasion and B point), AF-BF (distance from A point to B point in mm), L1-NB (distance from lower incisor to NB line in mm), anterior maxillary alveolar height, posterior maxillary alveolar height, overjet, H angle hard tissue, H angle soft tissue and lower lip to E plane (absolute correlation values from 0.277 to 0.711). In contrast, the increase in facial convexity was correlated with lower values of Pg. to N perpendicular and Pg. to NB (mm) (absolute correlation value -0.302 and -0.294 respectively). From the soft tissue measurements, H angles had a higher correlation with visual perception than facial contour angle, nasolabial angle, and lower lip to E plane. In conclusion, the findings of this study indicated that the correlation of cephalometric measurements with visual perception was less than expected. Only 29% of cephalometric measurements had a significant correlation with visual perception. Therefore, diagnosis based solely on cephalometric analysis can result in failure to meet the patient’s esthetic expectation.

Keywords: cephalometric measurements, facial profile, skeletal type II, visual perception

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Authors: Benniche Omar

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We are concerned with abstract fully nonlinear differential equations having the form y’(t)=Ay(t)+f(t,y(t)) where A is an m—dissipative operator (possibly multi—valued) defined on a subset D(A) of a Banach space X with values in X and f is a given function defined on I×X with values in X. We consider a graph K in I×X. We recall that K is said to be viable with respect to the above abstract differential equation if for each initial data in K there exists at least one trajectory starting from that initial data and remaining in K at least for a short time. The viability problem has been studied by many authors by using various techniques and frames. If K is closed, it is shown that a tangency condition, which is mainly linked to the dynamic, is crucial for viability. In the case when X is infinite dimensional, compactness and convexity assumptions are needed. In this paper, we are concerned with the notion of near viability for a given graph K with respect to y’(t)=Ay(t)+f(t,y(t)). Roughly speaking, the graph K is said to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)), if for each initial data in K there exists at least one trajectory remaining arbitrary close to K at least for short time. It is interesting to note that the near viability is equivalent to an appropriate tangency condition under mild assumptions on the dynamic. Adding natural convexity and compactness assumptions on the dynamic, we may recover the (exact) viability. Here we investigate near viability for a graph K in I×X with respect to y’(t)=Ay(t)+f(t,y(t)) where A and f are as above. We emphasis that the t—dependence on the perturbation f leads us to introduce a new tangency concept. In the base of a tangency conditions expressed in terms of that tangency concept, we formulate criteria for K to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)). As application, an abstract null—controllability theorem is given.

Keywords: abstract differential equation, graph, tangency condition, viability

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Authors: İbrahim Aktaş, Árpád Baricz

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In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function

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Authors: Miranda E. Karban

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A distinctive pattern of occipital squama convexity, known as the occipital bun or chignon, has traditionally been considered a derived Neandertal trait. However, some early modern and extant Homo sapiens share similar occipital bone morphology, showing pronounced internal and external occipital squama curvature and paralambdoidal flattening. It has been posited that these morphological patterns are homologous in the two groups, but this claim remains disputed. Many developmental hypotheses have been proposed, including assertions that the chignon represents a developmental response to a long and narrow cranial vault, a narrow or flexed basicranium, or a prognathic face. These claims, however, remain to be metrically quantified in a large subadult sample, and little is known about the feature’s developmental, functional, or evolutionary significance. This study assesses patterns of chignon development and covariation in a comparative sample of extant human growth study cephalograms. Cephalograms from a total of 549 European-derived North American subjects (286 male, 263 female) were scored on a 5-stage ranking system of chignon prominence. Occipital squama shape was found to exist along a continuum, with 34 subjects (6.19%) possessing defined chignons, and 54 subjects (9.84%) possessing very little occipital squama convexity. From this larger sample, those subjects represented by a complete radiographic series were selected for metric analysis. Measurements were collected from lateral and posteroanterior (PA) cephalograms of 26 subjects (16 male, 10 female), each represented at 3 longitudinal age groups. Age group 1 (range: 3.0-6.0 years) includes subjects during a period of rapid brain growth. Age group 2 (range: 8.0-9.5 years) includes subjects during a stage in which brain growth has largely ceased, but cranial and facial development continues. Age group 3 (range: 15.9-20.4 years) includes subjects at their adult stage. A total of 16 landmarks and 153 sliding semi-landmarks were digitized at each age point, and geometric morphometric analyses, including relative warps analysis and two-block partial least squares analysis, were conducted to study covariation patterns between midsagittal occipital bone shape and other aspects of craniofacial morphology. A convex occipital squama was found to covary significantly with a low, elongated neurocranial vault, and this pattern was found to exist from the youngest age group. Other tested patterns of covariation, including cranial and basicranial breadth, basicranial angle, midcoronal cranial vault shape, and facial prognathism, were not found to be significant at any age group. These results suggest that the chignon, at least in this sample, should not be considered an independent feature, but rather the result of developmental interactions relating to neurocranial elongation. While more work must be done to quantify chignon morphology in fossil subadults, this study finds no evidence to disprove the developmental homology of the feature in modern humans and Neandertals.

Keywords: chignon, craniofacial covariation, human cranial development, longitudinal growth study, occipital bun

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Authors: Fuad Al Sarari

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The purpose of the present paper is to study subclasses of analytic functions which generalize the classes of Janowski functions introduced by Polatoglu. We study certain convolution conditions. This leads to a study of the sufficient condition and the neighborhood results related to the functions in the class S (T; H; F ): and a study of new subclasses of analytic functions that are defined using notions of the generalized Janowski classes and -symmetrical functions. In the quotient of analytical representations of starlikeness and convexity with respect to symmetric points, certain inherent properties are pointed out.

Keywords: convolution conditions, subordination, Janowski functions, starlike functions, convex functions

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Authors: Androniki-Anna Doulgeroglou, Panagiotis Kotronis, Giulio Sciarra, Catherine Bouillon

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The interaction diagrams are functions that define ultimate states expressed in terms of generalized forces (axial force, bending moment and shear force). Two characteristic states for reinforced concrete (RC) sections are proposed: the first characteristic state corresponds to the yield of the reinforcement bars and the second to the peak values of the generalized forces generalized displacements curves. 3D numerical simulations are then conducted for RC columns and the global responses are compared to experimental results. Interaction diagrams for combined flexion, shear and axial force loading conditions are numerically produced for symmetrically RC square sections for different reinforcement ratios. Analytical expressions of the interaction diagrams are also proposed, satisfying the condition of convexity. Comparison with interaction diagrams from the Eurocode is finally presented for the study cases.

Keywords: analytical convex expressions, finite element method, interaction diagrams, reinforced concrete

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Authors: Arezoo Heidary, Abolfazl Mirzazadeh, Aref Gholami-Qadikolaei

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In the business environment it is very common that a lot received may not be equal to quantity ordered. in this work, a random disturbance in a received quantity is considered. It is assumed a maximum allowable limit for storage space and inventory investment.The impact of lead time and ordering cost reductions once they act dependently is also investigated. Further, considering a mixture of back order and lost sales for allowable shortage system, the effect of investment on reducing lost sale rate is analyzed. For the proposed control system, a Lagrangian method is applied in order to solve the problem and an algorithmic procedure is utilized to achieve optimal solution with the global minimum expected cost. Finally, proves on concavity and convexity of the model in the decision variables are shown.

Keywords: stochastic inventory system, lead time, ordering cost, lost sale rate, inventory constraints, random disturbance

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Authors: Sergey Podluzhnyy

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One of the most important tasks of investment and pension fund management is building decision support system which helps to make right decision on corporate bond portfolio formation. Today there are several basic methods of bond portfolio management. They are duration management, immunization and convexity management. Identified methods have serious disadvantage: they do not take into account credit risk or insolvency risk of issuer. So, identified methods can be applied only for management and evaluation of high-quality sovereign bonds. Applying article proposes mathematical model for building an optimal in case of risk and yield corporate bond portfolio. Proposed model takes into account the default probability in formula of assessment of bonds which results to more correct evaluation of bonds prices. Moreover, applied model provides tools for visualization of the efficient frontier of corporate bonds portfolio taking into account the exposure to credit risk, which will increase the quality of the investment decisions of portfolio managers.

Keywords: corporate bond portfolio, default probability, effective boundary, portfolio optimization task

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Authors: Iannick Gagnon, Alain April

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The performance of a metaheuristic on a given problem class depends on the class itself and the choice of parameters. Parameter tuning is the most time-consuming phase of the optimization process after the main calculations and it often nullifies the speed advantage of metaheuristics over traditional optimization algorithms. Several off-the-shelf parameter tuning algorithms are available, but when the objective function is expensive to evaluate, these can be prohibitively expensive to use. This paper presents a surrogate-like method for finding adequate parameters using fitness landscape analysis on simple benchmark functions and real-world objective functions. The result is a simple compound similarity metric based on the empirical correlation coefficient and a measure of convexity. It is then used to find the best benchmark functions to serve as surrogates. The near-optimal parameter set is then found using fractional factorial design. The real-world problem of NACA airfoil lift coefficient maximization is used as a preliminary proof of concept. The overall aim of this research is to reduce the computational overhead of metaheuristics parameterization.

Keywords: metaheuristics, stochastic optimization, particle swarm optimization, exploratory landscape analysis

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Authors: Apirak Sombat, Teerapol Saleewong, Poom Kumam, Parin Chaipunya, Wiyada Kumam, Anantachai Padcharoen, Yeol Je Cho, Thana Sutthibutpong

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This research is aimed to study a two-step iteration process defined over a finite family of σ-asymptotically quasi-nonexpansive nonself-mappings. The strong convergence is guaranteed under the framework of Banach spaces with some additional structural properties including strict and uniform convexity, reflexivity, and smoothness assumptions. With similar projection technique for nonself-mapping in Hilbert spaces, we hereby use the generalized projection to construct a point within the corresponding domain. Moreover, we have to introduce the use of duality mapping and its inverse to overcome the unavailability of duality representation that is exploit by Hilbert space theorists. We then apply our results for σ-asymptotically quasi-nonexpansive nonself-mappings to solve for ideal efficiency of vector optimization problems composed of finitely many objective functions. We also showed that the obtained solution from our process is the closest to the origin. Moreover, we also give an illustrative numerical example to support our results.

Keywords: asymptotically quasi-nonexpansive nonself-mapping, strong convergence, fixed point, uniformly convex and uniformly smooth Banach space

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Authors: Naragain Phumchusri, Kittitach Pongpairoj

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Overbooking is a very useful revenue management technique that could help reduce costs caused by either undersales or oversales. In this paper, we propose an overbooking model for two types of cars that can minimize the total cost for car rental service. With two types of cars, there is an upgrade possibility for lower type to upper type. This makes the model more complex than one type of cars scenario. We have found that convexity can be proved in this case. Sensitivity analysis of the parameters is conducted to observe the effects of relevant parameters on the optimal solution. Model simplification is proposed using multiple linear regression analysis, which can help estimate the optimal overbooking level using appropriate independent variables. The results show that the overbooking level from multiple linear regression model is relatively close to the optimal solution (with the adjusted R-squared value of at least 72.8%). To evaluate the performance of the proposed model, the total cost was compared with the case where the decision maker uses a naïve method for the overbooking level. It was found that the total cost from optimal solution is only 0.5 to 1 percent (on average) lower than the cost from regression model, while it is approximately 67% lower than the cost obtained by the naïve method. It indicates that our proposed simplification method using regression analysis can effectively perform in estimating the overbooking level.

Keywords: overbooking, car rental industry, revenue management, stochastic model

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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: Taleb L., Benarbia M., Boutira F. M., Allam H., Boukerche A.

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Introduction and purpose of the study: Meningiomas are the most common non-glial intracranial tumors in adults, accounting for approximately 30% of all central nervous system tumors. The aim of our study is to determine the epidemiological, clinical, therapeutic, and evolutionary characteristics of a cohort of patients with intracranial meningioma treated with radiotherapy at the Emir Abdelkader Cancer Center in Oran. Material and methods: This is a retrospective study of 44 patients during the period from 2014 to 2020. The overall survival and relapse-free survival curves were calculated using the Kaplan-Meier method. Results and statistical analysis: The median age of the patients was 49 years [21-76 years] with a clear female predominance (sex ratio=2.4). The average diagnostic delay was seven months [2 to 24 months], the circumstances of the discovery of which were dominated by headaches in 54.5% of cases (n=24), visual disturbances in 40.9% (n=18), and motor disorders in 15.9% (n=7). The seat of the tumor was essentially at the level of the base of the skull in 52.3% of patients (n=23), including 29.5% (n=13) at the level of the cavernous sinus, 27.3% (n=12) at the parasagittal level and 20.5% (n=9) at the convexity. The diagnosis was confirmed surgically in 36 patients (81.8%) whose anatomopathological study returned in favor of grades I, II, and III in respectively 40.9%, 29.5%, and 11.4% of the cases. Radiotherapy was indicated postoperatively in 45.5% of patients (n=20), exclusive in 27.3% (n=12) and after tumor recurrence in 27.3% of cases (n=18). The irradiation doses delivered were as follows: 50 Gy (20.5%), 54 Gy (65.9%), and 60 Gy (13.6%). With a median follow-up of 69 months, the probabilities of relapse-free survival and overall survival at three years are 93.2% and 95.4%, respectively, whereas they are 71.2% and 80.7% at five years. Conclusion: Meningiomas are common primary brain tumors. Most often benign but can also progress aggressively. Their treatment is essentially surgical, but radiotherapy retains its place in specific situations, allowing good tumor control and overall survival.

Keywords: diagnosis, meningioma, surgery, radiotherapy, survival

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Authors: Sunantha Teyarachakul

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We consider the worker-learning Newsvendor Model, under the case of lost-sales for unmet demand, with the research objective of proposing the cost-minimization order policy and lot size, scheduled to arrive at the beginning of the selling-period. In general, the New Vendor Model is used to find the optimal order quantity for the perishable items such as fashionable products or those with seasonal demand or short-life cycles. Technically, it is used when the product demand is stochastic and available for the single selling-season, and when there is only a one time opportunity for the vendor to purchase, with possibly of long ordering lead-times. Our work differs from the classical Newsvendor Model in that we incorporate the human factor (specifically worker learning) and its influence over the costs of processing units into the model. We describe this by using the well-known Wright’s Learning Curve. Most of the assumptions of the classical New Vendor Model are still maintained in our work, such as the constant per-unit cost of leftover and shortage, the zero initial inventory, as well as the continuous time. Our problem is challenging in the way that the best order quantity in the classical model, which is balancing the over-stocking and under-stocking costs, is no longer optimal. Specifically, when adding the cost-saving from worker learning to such expected total cost, the convexity of the cost function will likely not be maintained. This has called for a new way in determining the optimal order policy. In response to such challenges, we found a number of characteristics related to the expected cost function and its derivatives, which we then used in formulating the optimal ordering policy. Examples of such characteristics are; the optimal order quantity exists and is unique if the demand follows a Uniform Distribution; if the demand follows the Beta Distribution with some specific properties of its parameters, the second derivative of the expected cost function has at most two roots; and there exists the specific level of lot size that satisfies the first order condition. Our research results could be helpful for analysis of supply chain coordination and of the periodic review system for similar problems.

Keywords: inventory management, Newsvendor model, order policy, worker learning

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Authors: Fumihiro Ima, Shinichi Watanabe, Shingo Maeda, Haruna Imai, Hiroki Niimi

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It is important to know growth rate of brain tumors before surgery because it influences treatment planning including not only surgical resection strategy but also adjuvant therapy after surgery. Amide proton transfer (APT) imaging is an emerging molecular magnetic resonance imaging (MRI) technique based on chemical exchange saturation transfer without administration of contrast medium. The underlying assumption in APT imaging of tumors is that there is a close relationship between the proliferative activity of the tumor and mobile protein synthesis. We aimed to evaluate the diagnostic performance of APT imaging of pre-and post-treatment brain tumors. Ten patients with brain tumor underwent conventional and APT-weighted sequences on a 3.0 Tesla MRI before clinical intervention. The maximum and the minimum APT-weighted signals (APTWmax and APTWmin) in each solid tumor region were obtained and compared before and after clinical intervention. All surgical specimens were examined for histopathological diagnosis. Eight of ten patients underwent adjuvant therapy after surgery. Histopathological diagnosis was glioma in 7 patients (WHO grade 2 in 2 patients, WHO grade 3 in 3 patients and WHO grade 4 in 2 patients), meningioma WHO grade1 in 2 patients and primary lymphoma of the brain in 1 patient. High-grade gliomas showed significantly higher APTW-signals than that in low-grade gliomas. APTWmax in one huge parasagittal meningioma infiltrating into the skull bone was higher than that in glioma WHO grade 4. On the other hand, APTWmax in another convexity meningioma was the same as that in glioma WHO grade 3. Diagnosis of primary lymphoma of the brain was possible with APT imaging before pathological confirmation. APTW-signals in residual tumors decreased dramatically within one year after adjuvant therapy in all patients. APT imaging demonstrated excellent diagnostic performance for the planning of surgery and adjuvant therapy of brain tumors.

Keywords: amides, magnetic resonance imaging, brain tumors, cell proliferation

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Authors: Fumihiro Imai, Shinichi Watanabe, Shingo Maeda, Haruna Imai, Hiroki Niimi

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It is important to know the growth rate of brain tumors before surgery because it influences treatment planning, including not only surgical resection strategy but also adjuvant therapy after surgery. Amide proton transfer (APT) imaging is an emerging molecular magnetic resonance imaging (MRI) technique based on chemical exchange saturation transfer without the administration of a contrast medium. The underlying assumption in APT imaging of tumors is that there is a close relationship between the proliferative activity of the tumor and mobile protein synthesis. We aimed to evaluate the diagnostic performance of APT imaging of pre-and post-treatment brain tumors. Ten patients with brain tumor underwent conventional and APT-weighted sequences on a 3.0 Tesla MRI before clinical intervention. The maximum and the minimum APT-weighted signals (APTWmax and APTWmin) in each solid tumor region were obtained and compared before and after a clinical intervention. All surgical specimens were examined for histopathological diagnosis. Eight of ten patients underwent adjuvant therapy after surgery. Histopathological diagnosis was glioma in 7 patients (WHO grade 2 in 2 patients, WHO grade 3 in 3 patients, and WHO grade 4 in 2 patients), meningioma WHO grade 1 in 2 patients, and primary lymphoma of the brain in 1 patient. High-grade gliomas showed significantly higher APTW signals than that low-grade gliomas. APTWmax in one huge parasagittal meningioma infiltrating into the skull bone was higher than that in glioma WHO grade 4. On the other hand, APTWmax in another convexity meningioma was the same as that in glioma WHO grade 3. Diagnosis of primary lymphoma of the brain was possible with APT imaging before pathological confirmation. APTW signals in residual tumors decreased dramatically within one year after adjuvant therapy in all patients. APT imaging demonstrated excellent diagnostic performance for the planning of surgery and adjuvant therapy of brain tumors.

Keywords: amides, magnetic resonance imaging, brain tumors, cell proliferation

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Authors: Ali Essam El Shazly

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The Haussmannization plan of Cairo in 1867 formed a regular network of roundabout spaces, though deteriorated at present. The method of identifying the spatial structure of roundabout Cairo for conservation matches the voronoi diagram with the space syntax through their geometrical property of spatial convexity. In this initiative, the primary convex hull of first-order voronoi adopts the integral and control measurements of space syntax on Cairo’s roundabout generators. The functional essence of royal palaces optimizes the roundabout structure in terms of spatial measurements and the symbolic voronoi projection of 'Tahrir Roundabout' over the Giza Nile and Pyramids. Some roundabouts of major public and commercial landmarks surround the pole of 'Ezbekia Garden' with a higher control than integral measurements, which filter the new spatial structure from the adjacent traditional town. Nevertheless, the least integral and control measures correspond to the voronoi contents of pollutant workshops and the plateau of old Cairo Citadel with the visual compensation of new royal landmarks on top. Meanwhile, the extended suburbs of infinite voronoi polygons arrange high control generators of chateaux housing in 'garden city' environs. The point pattern of roundabouts determines the geometrical characteristics of voronoi polygons. The measured lengths of voronoi edges alternate between the zoned short range at the new poles of Cairo and the distributed structure of longer range. Nevertheless, the shortest range of generator-vertex geometry concentrates at 'Ezbekia Garden' where the crossways of vast Cairo intersect, which maximizes the variety of choice at different spatial resolutions. However, the symbolic 'Hippodrome' which is the largest public landmark forms exclusive geometrical measurements, while structuring a most integrative roundabout to parallel the royal syntax. Overview of the symbolic convex hull of voronoi with space syntax interconnects Parisian Cairo with the spatial chronology of scattered monuments to conceive one universal Cairo structure. Accordingly, the approached methodology of 'voronoi-syntax' prospects the future conservation of roundabout Cairo at the inferred city-level concept.

Keywords: roundabout Cairo, first-order Voronoi, space syntax, spatial structure

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Authors: Elham Kiyani

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In this paper, we first introduce the concept of Q-efficient solutions in a real linear space not necessarily endowed with a topology, where Q is some nonempty (not necessarily convex) set. We also used the scalarization technique including the Gerstewitz function generated by a nonconvex set to characterize these Q-efficient solutions. The algebraic concepts of interior and closure are useful to study optimization problems without topology. Studying nonconvex vector optimization is valuable since topological interior is equal to algebraic interior for a convex cone. So, we use the algebraic concepts of interior and closure to define Q-weak efficient solutions and Q-Henig proper efficient solutions of set-valued optimization problems, where Q is not a convex cone. Optimization problems with set-valued maps have a wide range of applications, so it is expected that there will be a useful analytical tool in optimization theory for set-valued maps. These kind of optimization problems are closely related to stochastic programming, control theory, and economic theory. The paper focus on nonconvex problems, the results are obtained by assuming generalized non-convexity assumptions on the data of the problem. In convex problems, main mathematical tools are convex separation theorems, alternative theorems, and algebraic counterparts of some usual topological concepts, while in nonconvex problems, we need a nonconvex separation function. Thus, we consider the Gerstewitz function generated by a general set in a real linear space and re-examine its properties in the more general setting. A useful approach for solving a vector problem is to reduce it to a scalar problem. In general, scalarization means the replacement of a vector optimization problem by a suitable scalar problem which tends to be an optimization problem with a real valued objective function. The Gerstewitz function is well known and widely used in optimization as the basis of the scalarization. The essential properties of the Gerstewitz function, which are well known in the topological framework, are studied by using algebraic counterparts rather than the topological concepts of interior and closure. Therefore, properties of the Gerstewitz function, when it takes values just in a real linear space are studied, and we use it to characterize Q-efficient solutions of vector problems whose image space is not endowed with any particular topology. Therefore, we deal with a constrained vector optimization problem in a real linear space without assuming any topology, and also Q-weak efficient and Q-proper efficient solutions in the senses of Henig are defined. Moreover, by means of the Gerstewitz function, we provide some necessary and sufficient optimality conditions for set-valued vector optimization problems.

Keywords: algebraic interior, Gerstewitz function, vector closure, vector optimization

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Authors: Stojan Kravanja, Andrej Ivanič, Tomaž Žula

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This contribution focuses on structural optimization in civil engineering using mixed integer non-linear programming (MINLP). MINLP is characterized as a versatile method that can handle both continuous and discrete optimization variables simultaneously. Continuous variables are used to optimize parameters such as dimensions, stresses, masses, or costs, while discrete variables represent binary decisions to determine the presence or absence of structural elements within a structure while also calculating discrete materials and standard sections. The optimization process is divided into three main steps. First, a mechanical superstructure with a variety of different topology-, material- and dimensional alternatives. Next, a MINLP model is formulated to encapsulate the optimization problem. Finally, an optimal solution is searched in the direction of the defined objective function while respecting the structural constraints. The economic or mass objective function of the material and labor costs of a structure is subjected to the constraints known from structural analysis. These constraints include equations for the calculation of internal forces and deflections, as well as equations for the dimensioning of structural components (in accordance with the Eurocode standards). Given the complex, non-convex and highly non-linear nature of optimization problems in civil engineering, the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm is applied. This algorithm alternately solves subproblems of non-linear programming (NLP) and main problems of mixed-integer linear programming (MILP), in this way gradually refines the solution space up to the optimal solution. The NLP corresponds to the continuous optimization of parameters (with fixed topology, discrete materials and standard dimensions, all determined in the previous MILP), while the MILP involves a global approximation to the superstructure of alternatives, where a new topology, materials, standard dimensions are determined. The optimization of a convex problem is stopped when the MILP solution becomes better than the best NLP solution. Otherwise, it is terminated when the NLP solution can no longer be improved. While the OA/ER algorithm, like all other algorithms, does not guarantee global optimality due to the presence of non-convex functions, various modifications, including convexity tests, are implemented in OA/ER to mitigate these difficulties. The effectiveness of the proposed MINLP approach is demonstrated by its application to various structural optimization tasks, such as mass optimization of steel buildings, cost optimization of timber halls, composite floor systems, etc. Special optimization models have been developed for the optimization of these structures. The MINLP optimizations, facilitated by the user-friendly software package MIPSYN, provide insights into a mass or cost-optimal solutions, optimal structural topologies, optimal material and standard cross-section choices, confirming MINLP as a valuable method for the optimization of structures in civil engineering.

Keywords: MINLP, mixed-integer non-linear programming, optimization, structures

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Authors: Helen Bartsch, Markus Feldmann

Abstract:

The dimensioning of steel structures subject to fatigue loads, such as wind turbines, bridges, masts and towers, crane runways and weirs or components in crane construction, is often dominated by fatigue verification. The fatigue details defined by the welded connections, such as butt or cruciform joints, longitudinal welds, welded-on or welded-in stiffeners, etc., are decisive. In Europe, the verification is usually carried out according to EN 1993-1-9 on a nominal stress basis. The basis is the detailed catalog, which specifies the fatigue strength of the various weld and construction details according to fatigue classes. Until now, a relation between fatigue classes and weld imperfection sizes is not included. Quality levels for imperfections in fusion-welded joints in steel, nickel, titanium and their alloys are regulated in EN ISO 5817, which, however, doesn’t contain direct correlations to fatigue resistances. The question arises whether some imperfections might be tolerable to a certain extent since they may be present in the test data used for detail classifications dating back decades ago. Although current standardization requires proof of satisfying limits of imperfection sizes, it would also be possible to tolerate welds with certain irregularities if these can be reliably quantified by non-destructive testing. Fabricators would be prepared to undertake carefully and sustained weld inspection in view of the significant economic consequences of such unfavorable fatigue classes. This paper presents investigations on the fatigue behavior of common welded details containing imperfections. In contrast to the common nominal stress concept, local fatigue concepts were used to consider the true stress increase, i.e., local stresses at the weld toe and root. The actual shape of a weld comprising imperfections, e.g., gaps or undercuts, can be incorporated into the fatigue evaluation, usually on a numerical basis. With the help of the effective notch stress concept, the fatigue resistance of detailed local weld shapes is assessed. Validated numerical models serve to investigate notch factors of fatigue details with different geometries. By utilizing parametrized ABAQUS routines, detailed numerical studies have been performed. Depending on the shape and size of different weld irregularities, fatigue classes can be defined. As well load-carrying welded details, such as the cruciform joint, as non-load carrying welded details, e.g., welded-on or welded-in stiffeners, are regarded. The investigated imperfections include, among others, undercuts, excessive convexity, incorrect weld toe, excessive asymmetry and insufficient or excessive throat thickness. Comparisons of the impact of different imperfections on the different types of fatigue details are made. Moreover, the influence of a combination of crucial weld imperfections on the fatigue resistance is analyzed. With regard to the trend of increasing efficiency in steel construction, the overall aim of the investigations is to include a more economical differentiation of fatigue details with regard to tolerance sizes. In the long term, the harmonization of design standards, execution standards and regulations of weld imperfections is intended.

Keywords: effective notch stress, fatigue, fatigue design, weld imperfections

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