Search results for: weak convergence

Authors: Giorgi Goguadze, Jakub Zajączkowski

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This paper is written due to overview the connection between fragile states and non-state actors, we should take into account that fragile states may vary from weak, failing and failed. In this paper we will discuss about two countries, one of them is weak (Colombia/ second one is already failed- Somalia. We will try to understand what feeds ill non-state actors such as: terrorist organizations, criminal entities and other cells in these countries, what threats are they representing and how to eliminate these dangers in both national and international scope. This paper is mainly based on literature overview and personal attitude and doesn’t claim to be in scientific chain.

Keywords: fragile States, terrorism, tribalism, Somalia

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Authors: Apoorva Vinod, Archana Mathur, Snehanshu Saha

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Though there exists a plethora of Activation Functions (AFs) used in single and multiple hidden layer Neural Networks (NN), their behavior always raised curiosity, whether used in combination or singly. The popular AFs –Sigmoid, ReLU, and Tanh–have performed prominently well for shallow and deep architectures. Most of the time, AFs are used singly in multi-layered NN, and, to the best of our knowledge, their performance is never studied and analyzed deeply when used in combination. In this manuscript, we experiment with multi-layered NN architecture (both on shallow and deep architectures; Convolutional NN and VGG16) and investigate how well the network responds to using two different AFs (Sigmoid-Tanh, Tanh-ReLU, ReLU-Sigmoid) used alternately against a traditional, single (Sigmoid-Sigmoid, Tanh-Tanh, ReLUReLU) combination. Our results show that using two different AFs, the network achieves better accuracy, substantially lower loss, and faster convergence on 4 computer vision (CV) and 15 Non-CV (NCV) datasets. When using different AFs, not only was the accuracy greater by 6-7%, but we also accomplished convergence twice as fast. We present a case study to investigate the probability of networks suffering vanishing and exploding gradients when using two different AFs. Additionally, we theoretically showed that a composition of two or more AFs satisfies Universal Approximation Theorem (UAT).

Keywords: activation function, universal approximation function, neural networks, convergence

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Authors: N. Moradian, E. Timofeev, R. Tahir

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In this work, startability of the Busemann intake family with weak/strong conical shock, as most efficient intakes, via overboard mass spillage method is theoretically analyzed. Masterix and Candifix codes are used to numerically simulate few models of this type of intake and verify the theoretical results. Portions of the intake corresponding to various flow capture angles are considered to have mass spillage in the starting process of this intake. This approach allows for overboard mass spillage via a V-shaped slot with the tip of V coinciding with the focal point of the Busemann flow. The theoretical results, achieved using two different theories, of self-started Busemann takes with weak/strong conical shock show that significant improve in intake startability using overboard spillage technique. The starting phenomena of Busemann intakes with weak conical shock and seven different capture angles are numerically simulated at freestream Mach number of 3 to find the minimum area ratios of self-started intakes. The numerical results confirm the theoretical ones achieved by authors.

Keywords: Busemann intake, conical shock, overboard spillage, startability

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Authors: Irina Maria Artinescu, Costin Radu Boldea, Eduard-Ionut Matei

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The paper is a comparative study of two classical variants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time in classical CPU and, alternatively, in parallel GPU implementation.

Keywords: convex feasibility problem, convergence analysis, inpainting, parallel projection methods

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Authors: Sang Hee Shin

Abstract:

The technical improving project is for using the domestic construction technology in the weak soil condition. The improved technology is applied directly under local construction site at OOO, OOO. Existing anchor technology was developed for the case of soft ground as N value 10 or less. In case of soft ground and heavy load, the attachment site per one strand is shortened due to the distributed interval so that the installation site is increased relatively and being economically infeasible. In addition, in case of high tensile load, adhesion phenomenon between wedge and block occurs. To solve these problems, it strengthens the function of the attached strands to treat a ‘bulbing’ on the strands. In the solution for minimizing the internal damage and strengthening the removal function, it induces lubricating action using the film and the attached film, and it makes the buffer structure using wedge lubricating structure and the spring. The technology is performed such as in-house testing and the field testing. The project can improve the reliability of the standardized quality technique. As a result, it intended to give the technical competitiveness.

Keywords: anchor, improving technology, removal anchor, soil reinforcement, weak soil

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Authors: Yuanyuan Wang, Chun Hui

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Drawing on social capital theory, this article discusses how individuals may utilize network ties to come up with creativity. Social capital theory elaborates how network ties enhances individual creativity from three dimensions: structural access, and relational and cognitive mechanisms. We categorize network ties into strong and weak in terms of tie strength. With less structural constraints, weak ties allow diverse and heterogeneous knowledge to prosper, further facilitating individuals to build up connections among diverse even distant ideas. On the other hand, strong ties with the relational mechanism of cooperation and trust may benefit the accumulation of psychological capital, ultimately to motivate and sustain creativity. We suggest that differential ties play different roles for individual creativity: Weak ties deliver informational benefit directly rifling individual creativity from informational resource aspect; strong ties offer solidarity benefits to reinforce psychological capital, which further inspires individual creativity engagement from a psychological viewpoint. Social capital embedded in network ties influence individuals’ informational acquisition, motivation, as well as cognitive ability to be creative. Besides, we also consider the moderating effects constraining the relatedness between network ties and creativity, such as knowledge articulability. We hypothesize that when the extent of knowledge articulability is low, that is, with low knowledge codifiability, and high dependency and ambiguity, weak ties previous serving as knowledge reservoir will not become ineffective on individual creativity. Two-wave survey will be employed in Mainland China to empirically test mentioned propositions.

Keywords: network ties, social capital, psychological capital, knowledge articulability, individual creativity

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Authors: Young Hee Geum

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In this paper,we develop the complex dynamics of a family of optimal fourth-order multiple-root solvers and plot their basins of attraction. Mobius conjugacy maps and extraneous fixed points applied to a prototype quadratic polynomial raised to the power of the known integer multiplicity m are investigated. A 300 x 300 uniform grid centered at the origin covering 3 x 3 square region is chosen to visualize the initial values on each basin of attraction in accordance with a coloring scheme based on their dynamical behavior. The illustrative basins of attractions applied to various test polynomials and the corresponding statistical data for convergence are shown to confirm the theoretical convergence.

Keywords: basin of attraction, conjugacy, fourth-order, multiple-root finder

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Authors: Sahar Mobeen, Anam Rafique, Irum Baig

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Acoustic echo cancellation in multichannel is a system identification application. In real time environment, signal changes very rapidly which required adaptive algorithms such as Least Mean Square (LMS), Leaky Least Mean Square (LLMS), Normalized Least Mean square (NLMS) and average (AFA) having high convergence rate and stable. LMS and NLMS are widely used adaptive algorithm due to less computational complexity and AFA used of its high convergence rate. This research is based on comparison of acoustic echo (generated in a room) cancellation thorough LMS, LLMS, NLMS, AFA and newly proposed average normalized leaky least mean square (ANLLMS) adaptive filters.

Keywords: LMS, LLMS, NLMS, AFA, ANLLMS

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Authors: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: Umar Yusuf Batsari

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Let E be a uniformly smooth and uniformly convex real Banach space and C be a nonempty, closed and convex subset of E. Let $V= \{S_i : C\to C, ~i=1, 2, 3\cdots N\}$ be a convex set of relatively nonexpansive mappings containing identity. In this paper, an iterative sequence obtained from CQ algorithm was shown to have strongly converge to a point $\hat{x}$ which is a common fixed point of relatively nonexpansive mappings in V and also solve the system of equilibrium problems in E. The result improve some existing results in the literature.

Keywords: relatively nonexpansive mappings, strong convergence, equilibrium problems, uniformly smooth space, uniformly convex space, convex set, kadec klee property

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Authors: H. Abderrezek, M. N. Harmas

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DC-DC converters are widely used as reliable power source for many industrial and military applications, computers and electronic devices. Several control methods were developed for DC-DC converters control mostly with asymptotic convergence. Synergetic control (SC) is a proven robust control approach and will be used here in a so-called terminal scheme to achieve finite time convergence. Lyapunov synthesis is adopted to assure controlled system stability. Furthermore particle swarm optimization (PSO) algorithm, based on an integral time absolute of error (ITAE) criterion will be used to optimize controller parameters. Simulation of terminal synergetic control of a DC-DC converter is carried out for different operating conditions and results are compared to classic synergetic control performance, that which demonstrate the effectiveness and feasibility of the proposed control method.

Keywords: DC-DC converter, PSO, finite time, terminal, synergetic control

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Authors: Arbolino Roberta, Boffardi Raffaele

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Achieving the highest effectiveness for the National Plans for Recovery and Resilience (NPRR) while strengthening the objectives of cohesion and reduction of intra-EU unbalances is only possible by means of strategic, coordinated, and coherent policy planning. Therefore, the present research aims at assessing and quantifying the potential impact of NPRRs across the twenty-seven European Member States in terms of economic convergence, considering disaggregated data on industrial, construction, and service sectors. The first step of the research involves a performance analysis of the main macroeconomic indicators describing the trends of twenty-seven EU economies before the pandemic outbreak. Subsequently, in order to define the potential effect of the resources allocated, we perform an impact analysis of previous similar EU investment policies, estimating national-level sectoral elasticity associated with the expenditure of the 2007-2013 and 2014-2020 Cohesion programmes funds. These coefficients are then exploited to construct adjustment scenarios. Finally, convergence analysis is performed on the data used for constructing scenarios in order to understand whether the expenditure of funds might be useful to foster economic convergence besides driving recovery. The results of our analysis show that the allocation of resources largely mirrors the aims of the policy framework underlying the NPRR, thus reporting the largest investments in both those sectors most affected by the economic shock (services) and those considered fundamental for the digital and green transition. Notwithstanding an overall positive effect, large differences exist among European countries, while no convergence process seems to be activated or fostered by these interventions.

Keywords: NPRR, policy evaluation, cohesion policy, scenario Nalsysi

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Authors: Abdul Majid, Alia Jabeen, Nimra Zulifqar

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The inorganic molecular crystal (IMCs) due to their unusual structure has grabbed a lot of attention due to anisotropy in crystal structure. The IMCs consist of the molecular structures joined together via weak forces. Therefore, a difference between the bonding between the inter-cage and intra-cage interactions exists. To look closely at the bonding and interactions, we investigated interactions between two cages of Sb2O3 structure. The interactions were characterized via Extended Transition State-Natural Orbital for Chemical Valence-method (ETS-NOCV), Natural Bond Orbitals (NBO) and Quantum Theory of Atoms in Molecules (QTAIM). The results revealed strong intra-cage covalent bonding while weak van der Waals (vdWs) interactions along inter-cages exits. This structure cannot be termed as layered material although they have anisotropy in bonding and presence of weak vdWs interactions but its bulk is termed as inorganic layered clusters. This is due to the fact that the free standing sheet/films with these materials are not possible. This type of structures may be the most feasible to be used for the system to deal with high pressures and stress bearing materials.

Keywords: inorganic molecular crystals, density functional theory, cages, interactions

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Authors: Mohammed Belloufi, Rachid Benzine, Badreddine Sellami

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Conjugate gradient methods is useful for solving large scale optimization problems in scientific and engineering computation, characterized by the simplicity of their iteration and their low memory requirements. It is well known that the search direction plays a main role in the line search method. In this paper, we propose a search direction with the Wolfe line search technique for solving unconstrained optimization problems. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. Numerical results and comparisons with other CG methods are given.

Keywords: unconstrained optimization, conjugate gradient method, strong Wolfe line search, global convergence

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Authors: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: T. A. Biala

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This paper deals with the numerical integration of the general second order multipoint boundary value problems. This has been achieved by the development of a continuous linear multistep method (LMM). The continuous LMM is used to construct a main discrete method to be used with some initial and final methods (also obtained from the continuous LMM) so that they form a discrete analogue of the continuous second order boundary value problems. These methods are used as boundary value methods and adapted to cope with the integration of the general second order multipoint boundary value problems. The convergence, the use and the region of absolute stability of the methods are discussed. Several numerical examples are implemented to elucidate our solution process.

Keywords: linear multistep methods, boundary value methods, second order multipoint boundary value problems, convergence

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Authors: Z. Bouchama, N. Essounbouli, A. Hamzaoui, M. N. Harmas

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A new robust finite time synergetic controller is presented based on recently developed synergetic control methodology and a terminal attractor technique. A Fast Terminal Synergetic Control (FTSC) is proposed for controlling DC-DC buck converter. Unlike Synergetic Control (SC) and sliding mode control, the proposed control scheme has the characteristics of finite time convergence and chattering free phenomena. Simulation of stabilization and reference tracking for buck converter systems illustrates the approach effectiveness while stability is assured in the Lyapunov sense and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability.

Keywords: dc-dc buck converter, synergetic control, finite time convergence, terminal synergetic control, fast terminal synergetic control, Lyapunov

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Authors: Hulya Tuba Kiyan, Nilgun Ozturk

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Gentiana, a member of Gentianaceae, is represented by approximately 400 species in the world and 12 species in Turkey. Flavonoids, iridoids, triterpenoids and also xanthones are the major compounds of this genus, have been previously reported to have antiinflammatory, antimicrobial, antioxidant, hepatoprotective, hypotensive, hypoglycaemic, DNA repair and immunomodulatory properties. The methanolic extract of the aerial parts of Gentiana brachyphylla Vill. from Turkey was evaluated for its biological activities and its total phenolic content in the present study. According to the antioxidant activity results, G. brachyphylla methanolic extract showed very strong anti-DNA damage antioxidant activity with an inhibition of 81.82%. It showed weak ferric-reducing power with a EC50 value of 0.65 when compared to BHT (EC50 = 0.2). Also, at 0.5 mg/ml concentration, the methanolic extract inhibited ABTS radical cation activity with an inhibition of 20.13% when compared to Trolox (79.01%). Chelating ability of G. brachyphylla was 44.71% whereas EDTA showed 78.87% chelating activity at 0.2 mg/ml. Also G. brachyphylla showed weak 27.21% AChE, 20.23% BChE, strong 67.86% MAO-A and moderate 50.06% MAO-B, weak 19.14% COX-1, 29.11% COX-2 inhibitory activities at 0.25 mg/ml. The total phenolic content of G. brachyphylla was 156.23 ± 2.73 mg gallic acid equivalent/100 g extract.

Keywords: antioxidant activity, cholinesterase inhibitory activity, Gentiana brachyphylla Vill., total phenolic content

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Authors: Jinhui Bak, Bumjin Kim

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The purpose of this study is to analyze how the scientific and mathematical fields (STEM) and liberal arts (A) work together in the STEAM program. In the future STEAM programs that have been designed and developed, the humanities will act not just as a 'tool' for science technology and mathematics, but as a 'core' content to have an equivalent status. STEAM was first introduced to the Republic of Korea in 2011 when the Ministry of Education emphasized fostering creative convergence talent. Many programs have since been developed under the name STEAM, but with the majority of programs focusing on technology education, arts and humanities are considered secondary. As a result, arts is most likely to be accepted as an option that can be excluded from the teachers who run the STEAM program. If what we ultimately pursue through STEAM education is in fostering STEAM literacy, we should no longer turn arts into a tooling area for STEM. Based on this consciousness, this study analyzed over 160 STEAM programs in middle and high schools, which were produced and distributed by the Ministry of Education and the Korea Science and Technology Foundation from 2012 to 2017. The framework of analyses referenced two criteria presented in the related prior studies: normative convergence and technological convergence. In addition, we divide Arts into fine arts and liberal arts and focused on Korean Language Course which is in liberal arts and analyzed what kind of curriculum standards were selected, and what kind of process the Korean language department participated in teaching and learning. In this study, to ensure the reliability of the analysis results, we have chosen to cross-check the individual analysis results of the two researchers and only if they are consistent. We also conducted a reliability check on the analysis results of three middle and high school teachers involved in the STEAM education program. Analyzing 10 programs selected randomly from the analyzed programs, Cronbach's α .853 showed a reliable level. The results of this study are summarized as follows. First, the convergence ratio of the liberal arts was lowest in the department of moral at 14.58%. Second, the normative convergence is 28.19%, which is lower than that of the technological convergence. Third, the language and achievement criteria selected for the program were limited to functional areas such as listening, talking, reading and writing. This means that the convergence of Korean language departments is made only by the necessary tools to communicate opinions or promote scientific products. In this study, we intend to compare these results with the STEAM programs in the United States and abroad to explore what elements or key concepts are required for the achievement criteria for Korean language and curriculum. This is meaningful in that the humanities field (A), including Korean, provides basic data that can be fused into 'equivalent qualifications' with science (S), technical engineering (TE) and mathematics (M).

Keywords: Korean STEAM Programme, liberal arts, STEAM curriculum, STEAM Literacy, STEM

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Authors: Julia Gurol

Abstract:

Why do we observe a shift towards convergence in EU-China security interests? While contradicting attitudes towards key principles of inter-state and region-to-state relations, including state sovereignty, territorial integrity, and intervention policies have ever since hindered EU-China inter-regional cooperation beyond the economic realm, collaboration in peace and security issues is now becoming a key pillar of European-Chinese relations. In addition, the Belt and Road Initiative as most ambitious Chinese foreign policy project explicitly touches upon several European foreign policy and security preferences. Based on these counterintuitive findings, this paper traces the process of convergence of Sino-European security interests. Drawing on qualitative text analysis of official Chinese and European policy papers and documents from the establishment of diplomatic relations in 1975 until today, it assesses the striking change over time. On this basis, the paper uses theories of neo-functionalism, inter-regionalism, and securitization and borrows from constructivist views in International Relations’ theory, to expound possible motives for the change in Chinese and respectively European preferences in the security realm. The results reveal interesting insights into the decisive factors and motives behind both countries’ foreign policies. The paper concludes with a discussion of further potential and difficulties of EU-China security cooperation.

Keywords: belt and road initiative, China, European Union, foreign policy, neo-functionalism, security

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Authors: Yexin Qu

Abstract:

Izafe is a construction typically found in Iranian languages, which is attested already in Old Avestan and Old Persian. The narrow sense of izafe can be described as the linear structure of [NP pt Modifier] with pt as an uninflectable particle or clitic. The history of the Iranian izafe has the following stages: Stage I: Verbless nominal relative clauses, Stage II: Verbless nominal relative clauses with Case Attraction; and Stage III: Narrow sense izafe. Previous works suggest that embedded relative clauses and correlatives in other Indo-European languages might be relevant for the source of the izafe-construction. Stage I, as the precursor of narrow sense izafe, or so-called “prezafe” is not found in branches other than Iranian. Comparable cases have been demonstrated in Vedic, Greek, and some rare cases in Latin. This suggests “prezafe” may date back very early in Indo-European. Izafe-like structures are not attested in branches such as Balto-Slavic and Germanic, but Balto-Slavic definite adjectives and Germanic weak adjectives can be compared to the verbless nominal relative clauses and analyzed as developments of verbless relative clauses parallel to izafe in Indo-Iranian, as are called “parizafe” in this paper. In this paper, the verbless RC is compared with Germanic weak adjectives. The Germanic languages used n-stem derivation to form determined derivatives, which are semantically equivalent to the appositive RC and eventually became weak adjectives. To be more precise, starting from an adjective “X”, the Germanic weak adjective structure is formed as [det X-n], literally “the X”, with the meaning “the X one”, which can be shown to be semantically equivalent to “the one which is X”. In this paper, Stage I suggest that, syntactically, the Germanic verbless relative clauses went through CP to DP relabeling like Iranian, based on the following observations: (1) Germanic relative pronouns (e.g., Gothic saei, Old English se) and determiners (e.g., Gothic sa, Old English se) are both from the *so/to pronominal roots; (2) the semantic equivalence of Germanic weak adjectives and the izafe structure. This may suggest that Germanic may also have had “Prezafe” Stages I and II. In conclusion: “Prezafe” in Stage I may have been a phenomenon of the proto-language, Stage II was the result of independent parallel developments and then each branch had its own strategy.

Keywords: izafe, relative clause, Germanic, Indo-European

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Authors: Bastien Batardière, Joon Kwon

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For finite-sum optimization, variance-reduced gradient methods (VR) compute at each iteration the gradient of a single function (or of a mini-batch), and yet achieve faster convergence than SGD thanks to a carefully crafted lower-variance stochastic gradient estimator that reuses past gradients. Another important line of research of the past decade in continuous optimization is the adaptive algorithms such as AdaGrad, that dynamically adjust the (possibly coordinate-wise) learning rate to past gradients and thereby adapt to the geometry of the objective function. Variants such as RMSprop and Adam demonstrate outstanding practical performance that have contributed to the success of deep learning. In this work, we present AdaLVR, which combines the AdaGrad algorithm with loopless variance-reduced gradient estimators such as SAGA or L-SVRG that benefits from a straightforward construction and a streamlined analysis. We assess that AdaLVR inherits both good convergence properties from VR methods and the adaptive nature of AdaGrad: in the case of L-smooth convex functions we establish a gradient complexity of O(n + (L + √ nL)/ε) without prior knowledge of L. Numerical experiments demonstrate the superiority of AdaLVR over state-of-the-art methods. Moreover, we empirically show that the RMSprop and Adam algorithm combined with variance-reduced gradients estimators achieve even faster convergence.

Keywords: convex optimization, variance reduction, adaptive algorithms, loopless

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Authors: Amal Ezzidani, Abdelghani Ben Tahar, Mohamed Hanini

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A sequence of finite tandem queue is considered for this study. Each one has a single server, which operates under the egalitarian processor sharing discipline. External customers arrive at each queue according to a renewal input process and having a general service times distribution. Upon completing service, customers leave the current queue and enter to the next. Under mild assumptions, including critical data, we prove the existence and the uniqueness of the fluid solution. For asymptotic behavior, we provide necessary and sufficient conditions for the invariant state and the convergence to this invariant state. In the end, we establish the convergence of a correctly normalized state process to a fluid limit characterized by a system of algebraic and integral equations.

Keywords: fluid limit, fluid model, measure valued process, processor sharing, tandem queue

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Authors: B. Sellami, M. Belloufi

Abstract:

Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, we propose a new two-parameter family of conjugate gradient methods for unconstrained optimization. The two-parameter family of methods not only includes the already existing three practical nonlinear conjugate gradient methods, but also has other family of conjugate gradient methods as subfamily. The two-parameter family of methods with the Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for the two-parameter family of methods. The numerical results show that this method is efficient for the given test problems. In addition, the methods related to this family are uniformly discussed.

Keywords: unconstrained optimization, conjugate gradient method, line search, global convergence

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Igor Velickovski, Aleksandar Stojkov, Ivana Rajkovic

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This paper investigates drivers of shock synchronization using quarterly data for 27 European countries over the period 1999-2013 and taking into account the difference between core (‘the euro area core locomotive’) and peripheral euro area and transition countries (‘the peripheral wagons’). Results from panel error-correction models suggest that core of the euro area has not been strong magnetizer of the shock convergence of periphery and transition countries since the euro inception as a result of the offsetting effects of the various factors that affected the shock convergence process. These findings challenge the endogeneity hypothesis in the optimum currency area framework and rather support the specialisation paradigm which is concerning evidence for the future stability of the euro area.

Keywords: dynamic panel models, shock synchronisation, trade, optimum currency area

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Authors: Sandeep Singh

Abstract:

In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: R. Sabre

Abstract:

This work focuses on the symmetric alpha stable process with continuous time frequently used in modeling the signal with indefinitely growing variance, often observed with an unknown additive error. The objective of this paper is to estimate this error from discrete observations of the signal. For that, we propose a method based on the smoothing of the observations via Jackson polynomial kernel and taking into account the width of the interval where the spectral density is non-zero. This technique allows avoiding the “Aliasing phenomenon” encountered when the estimation is made from the discrete observations of a process with continuous time. We have studied the convergence rate of the estimator and have shown that the convergence rate improves in the case where the spectral density is zero at the origin. Thus, we set up an estimator of the additive error that can be subtracted for approaching the original signal without error.

Keywords: spectral density, stable processes, aliasing, non parametric

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Authors: Belloufi Mohammed, Sellami Badreddine

Abstract:

Conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. In this work, we propose a new class of conjugate gradient methods which ensures sufficient descent. Moreover, we propose a new search direction with the Wolfe line search technique for solving unconstrained optimization problems, a global convergence result for general functions is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments indicate that our proposed methods are preferable and in general superior to the classical conjugate gradient methods in terms of efficiency and robustness.

Keywords: unconstrained optimization, conjugate gradient method, sufficient descent property, numerical comparisons

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