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In this paper, we aim to solving the open question left in [Nie, Yuan: Nonlinear Anal 196 (2020); J. Math. Anal. Appl 505 (2022) and Xiao, Fei: J. Math. Anal. Appl 514 (2022)]. We prove that a multidimensional chemotaxis system is ill-posedness in B ˙ 2 d , r - 3 2 × ( B ˙ 2 d , r - 1 2 ) d when 1 ≤ r < d due to the lack of continuity of the solution. [ABSTRACT FROM AUTHOR]

This special issue of the Journal Mathematical Methods in the Applied Sciences on the topic of Modelling, Analysis, and Applications is devoted to the development of mathematical modelling, analysis, and applications, from theoretical and numerical perspectives, involving different applied sciences and engineering. It collects invited contributions, from selected quality full papers submitted to the International Conference on Mathematical Analysis and Applications in Science and Engineering (ICMA2SC2022). The conference took place in Porto, Portugal in 27–29 June 2022 (https://www.isep.ipp.pt/Page/ViewPage/ICMASC). [ABSTRACT FROM AUTHOR]

In the literature, rank-constrained Hermitian nonnegative-definite solutions to the matrix equation AXAH=B have been investigated, under the conditions that B is Hermitian and nonnegative-definite, and the matrix equation is consistent. In this paper, we discuss rank-constrained Hermitian nonnegative-definite least squares solutions to this matrix equation, in which the above conditions may not hold. We derive the rank range and expression of these least squares solutions. Therefore, the results obtained in this paper generalize those in the literature. [ABSTRACT FROM AUTHOR]

Rufus P. Isaacs joined the RAND Corporation4. Santa Monica, California in 1948 and started to develop the theory of dynamic games in the early 1950s. Until winter 1954/55, when Isaacs left the RAND Corporation, he investigated two player. zero-sum dynamic games of the classic pursuit-evasion type. Prior to 1965, Isaacs published his theory only in internal RAND papers and research memoranda. In his first RAND paper (Ref. 1), Isaacs sketched the basic ideas of zero-sum dynamic game theory The ideas already included rudimentary precursors of the maximum principle, dynamic programming, and backward analysis. At the end of 1954 and the beginning of 1955. Isaacs summarized his research in four research memoranda (Refs. 3–6), which ten years later formed the basis of his famous book on Differential Games (Ref. 7). This paper survey's Isaacs' research with an emphasis on the early years of dynamic games. The readers are kindly invited to discuss the author's point of view. Comments and statements sent to the author will be summarized and published later. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system. [ABSTRACT FROM AUTHOR]

This is a reply to Ramon Ferrer-I-Cancho's paper in this issue "Some Word Order Biases from Limited Brain Resources: A Mathematical Approach." In this reply, I challenge the Euclidean distance model proposed in that paper by proposing a simple alternative model based on linear ordering. [ABSTRACT FROM AUTHOR]

Compositional verification is essential to address state explosion in model checking. Traditionally, an over-approximate context is needed for each individual component in a system for sound verification. This may cause state explosion for the intermediate results as well as inefficiency for abstraction refinement. This paper presents an opposite approach, a compositional reachability method, which constructs the state space of each component from an under-approximate context gradually until a counter-example is found or a fixpoint in state space is reached. This method has an additional advantage in that counter-examples, if there are any, can be found much earlier, thus leading to faster verification. Furthermore, this modular verification framework does not require complex compositional reasoning rules. The experimental results indicate that this method is promising. [ABSTRACT FROM AUTHOR]

It is shown in the paper [1] that every generalized topology can be generated by a generalized neighbourhood system. Following the paper [3], we discuss some questions related to this construction. [ABSTRACT FROM AUTHOR]

In recent years, wavelet shrinkage has become a very appealing method for data de-noising and density function estimation. In particular, Bayesian modelling via hierarchical priors has introduced novel approaches for Wavelet analysis that had become very popular, and are very competitive with standard hard or soft thresholding rules. In this sense, this paper proposes a hierarchical prior that is elicited on the model parameters describing the wavelet coefficients after applying a Discrete Wavelet Transformation (DWT). In difference to other approaches, the prior proposes a multivariate Normal distribution with a covariance matrix that allows for correlations among Wavelet coefficients corresponding to the same level of detail. In addition, an extra scale parameter is incorporated that permits an additional shrinkage level over the coefficients. The posterior distribution for this shrinkage procedure is not available in closed form but it is easily sampled through Markov chain Monte Carlo (MCMC) methods. Applications on a set of test signals and two noisy signals are presented. [ABSTRACT FROM AUTHOR]

For any C¹ differential system S on a compact Riemannian manifold M of dimension d with d ≥= 2, this paper studies the Liao style numbers, κ(S) (or respectively, κ*(S)) of S from the view-point of ergodic theory. Here κ(S) (κ* (S)) is the largest number of moving vectors (or respectively, conjugate-) of the differential system S that are mean linearly independent. For any ergodic measure v of S, two positive integers κ* (v) and κ(v), called the reduced and non-reduced style number of v respectively, are introduced. The connection between the style numbers of the system (M, S) and ones of the ergodic system (M, S; v) are discovered by the variational principle of style number proved in the paper. Several characterization theorems with respect to the style numbers κ* (S), κ*(v), κ(S) and κ(v) are presented respectively. [ABSTRACT FROM AUTHOR]

The maximal covering location problem has been shown to be a useful tool in siting emergency services. In this paper we expand the model along two dimensions - workload capacities on facilities and the allocation or multiple levels of backup or prioritized service for all demand points. In emergency service facility location decisions such as ambulance sitting, when all of a facility's resources are needed to meet each call for service and the demand cannot be queued, the need for a backup unit may be required. This need is especially significant in areas of high demand. These areas also will often result in excessive workload for some facilities. Effective siting decisions, therefore, must address both the need for a backup response facility for each demand point and a reasonable limit on each facility's workload. In this paper, we develop a model which captures these concerns as well as present an efficient solution procedure using Lagrangian relaxation. Results of extensive computational experiments are presented to demonstrate the viability of the approach. [ABSTRACT FROM AUTHOR]

The article is a comment on an article "Matrix Theory and Cost Allocation," by researchers T.H. Williams and C.H. Griffin, published in the July 1964 issue of the journal "The Accounting Review." According to the author, Williams and Griffin were the first to select this topic as an illustration of the application of matrix algebra to accounting problems. The model presented by Williams and Griffin is a matrix formulation of the popular simultaneous equations method of past years. It was pointed out that the aggregate cost of service departments after allocation in the Williams and Griffin model is more than the combined direct cost before allocation. The scope of this paper has two dimensions: first, to attempt to clarify the matrix algebra approaches that have already been posed and place them in perspective; second, to present a new matrix model of reciprocal service cost allocation and relate it to those previously presented. It would be assumed that each service department will have some of its cost allocated to some of the producing departments.

In this paper we continue the study, from Frittaion, Steila and Yokoyama (2017, Theory and Applications of Models of Computation 14th Annual Conference, Bern, Switzerland, April 20–22, 2017), on size-change termination (SCT) in the context of Reverse Mathematics. We analyse the soundness of the SCT method. In particular, we prove that the statement ‘any programme which satisfies the combinatorial condition provided by the SCT criterion is terminating’ is equivalent to WO(ω 3) over RCA 0 . [ABSTRACT FROM AUTHOR]

In this paper we investigate the Parisian ruin problem of the general dual Lévy risk model. Unlike the usual concept of ultimate ruin, allowing the surplus level to be negative within a prespecified period indicates that the deficit at Parisian ruin is not necessarily equal to zero. Hence, we consider a Gerber–Shiu type expected discounted penalty function at the Parisian ruin and obtain an explicit expression for this function under the dual Lévy risk model. As particular cases, we calculate the Parisian ruin probability and the expected discounted kth moments of the deficit at the Parisian ruin for the compound Poisson dual risk model and a drift-diffusion model. Numerical examples are given to illustrate the behavior of Parisian ruin and the expected discounted deficit at Parisian ruin. [ABSTRACT FROM AUTHOR]

In this paper, we propose a decentralized parallel computation model for global optimization using interval analysis. The model is adaptive to any number of processors and the workload is automatically and evenly distributed among all processors by alternative message passing. The problems received by each processor are processed based on their local dominance properties, which avoids unnecessary interval evaluations. Further, the problem is treated as a whole at the beginning of computation so that no initial decomposition scheme is required. Numerical experiments indicate that the model works well and is stable with different number of parallel processors, distributes the load evenly among the processors, and provides an impressive speedup, especially when the problem is time-consuming to solve. [ABSTRACT FROM AUTHOR]

Profile likelihood is a popular method of estimation in the presence of an infinite-dimensional nuisance parameter, as the method reduces the infinite-dimensional estimation problem to a finite-dimensional one. In this paper we investigate the efficiency of a semi-parametric maximum likelihood estimator based on the profile likelihood. By introducing a new parametrization, we improve on the seminal work of Murphy and van der Vaart ( J Am Stat Assoc, 95: 449-485, 2000): our improvement establishes the efficiency of the estimator through the direct quadratic expansion of the profile likelihood, which requires fewer assumptions. To illustrate the method an application to two-phase outcome-dependent sampling design is given. [ABSTRACT FROM AUTHOR]

This paper considers the problem of searching for the actual time of failure for a system when the only information that is available is that it is has failed by a time t. This situation can be analyzed by using the concept of the reversed failure rate. This paper considers optimization problems that can be solved by using the reversed failure rate. When a unit is detected to have failed at time t, we discuss an optimum backward time from time t to search for its failure time which minimizes the expected cost. The recovery of a database system and of reweighing products using a scale are taken to be two typical applications of the backward time concept. Two models are proposed for appropriate maintenance actions for these situations when a unit is detected to have failed at time t. [ABSTRACT FROM AUTHOR]

Relaxed controls have proved to be very useful in studying the existence of optimal controls in optimal control theory. Many positive results have been obtained in the literature. However, negative results have also made their rare appearances. The optimal control problem considered in this paper looks quite simple. Yet, by treating such a problem, we can get interesting results, substantiating our idea as to whether an optimal control exists or not. In our opinion, the method used in the paper can be applied to more generalized cases. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm which, for a given compact orientable irreducible boundary irreducible 3-manifold M, verifies whether M contains an essential orientable surface (possibly, with boundary), whose genus is at most N. The algorithm is based on Haken’s theory of normal surfaces, and on a trick suggested by Jaco and consisting in estimating the mean length of boundary curves in an unknown essential surface of a given genus in the given manifold. [ABSTRACT FROM AUTHOR]

In the paper, using the Adyan-Lysenok theorem claiming that, for any odd number n ≥ 1003, there is an infinite group each of whose proper subgroups is contained in a cyclic subgroup of order n, it is proved that the set of groups with this property has the cardinality of the continuum (for a given n). Further, it is proved that, for m ≥ k ≥ 2 and for any odd n ≥ 1003, the m-generated free n-periodic group is residually both a group of the above type and a k-generated free n-periodic group, and it does not satisfy the ascending and descending chain conditions for normal subgroups either. [ABSTRACT FROM AUTHOR]

A new evolving network based on the scale-free network of Barabási and Albert (BA) is studied, and the accelerated attachment of new edges is considered in its evolving process. The accelerated attachment is different from the previous accelerated growth of edges and has two particular meanings in this paper. One is that a new vertex with the edges is inserted into the network with acceleration at each time step; the other is that, with a given probability, some additional edges are linked with the vertices in proportion to the number of their obtained edges in the latest evolving periods. The new model describes the cases of those complex networks with a few exceptional vertices. The attachment mechanism of the new adding edges for these vertices does not follow the preferential attachment rule. Comparing with the linear edge growth model, the characteristics of the accelerated growth model are studied theoretically and numerically. We show that the degree distributions of these models have a power law decay and the exponents are larger than that of the BA model. We point out that the characteristics of the exceptional vertices and the aging vertices in an aging network are not identical. The reasons for neglecting this attachment in most of evolving networks are also summarized. [ABSTRACT FROM AUTHOR]

Nonlinear systems of time dependent partial differential equations of real life phenomena tend to be very complicated to solve numerically. One common approach to solve such problems is by applying operator splitting which introduces subproblems that are easier to handle. The solutions of the subsystems are usually glued together by either the Godunov method (first-order) or the Strang method (second-order). However, the accuracy of such an approach may be very hard to analyse because of the complexity of the equations involved. The purpose of the present paper is to introduce another line of reasoning concerning the accuracy of operator splitting. Let us assume that a fully coupled and implicit discretization of the complete system has been developed. Under appropriate conditions on the continuous problem, such discretizations provide reasonable and convergent approximations. As in the continuous case, operator splitting can be utilized to obtain tractable algebraic subsystems. The problem we address in the present paper is to obtain a bound on the difference between the fully coupled implicit discrete solutions, uh, and the solutions, uh, s, obtained by applying operator splitting to these discrete equations. Suppose we know that uh converges to the analytical solution u as the grid is properly refined and, applying the results from this paper, that uh, s converges toward uh under grid refinement. Then, by the triangle inequality, also the splitting approximation uh, s converges toward the analytical solution u and convergence is thus obtained for an approximation that, from a practical point of view, is easier to compute. [ABSTRACT FROM AUTHOR]

This paper gives a new way of showing that certain constant degree graphs are graph expanders. This is done by giving new proofs of expansion for three permutations of the Gabber-Galil expander. Our results give an expansion factor of (Multiple line equation(s) cannot be represented in ASCII text) for subgraphs of these three-regular graphs with (p - 1)² inputs for p prime. The proofs are not based on eigenvalue methods or higher algebra. The same methods show the expected number of probes for unsuccessful search in double hashing is bounded by (Multiple line equation(s) cannot be represented in ASCII text), where a is the load factor. This assumes a double hashing scheme in which two hash functions are randomly and independently chosen from a specified uniform distribution. The result is valid regardless of the distribution of the inputs. This is analogous to Carter and Wegman's result for hashing with chaining. This paper concludes by elaborating on how any sufficiently sized subset of inputs in any distribution expands in the subgraph of the Gabber-Galil graph expander of focus. This is related to any key distribution having expected (Multiple line equation(s) cannot be represented in ASCII text) probes for unsuccessful search for double hashing given the initial random, independent, and uniform choice of two universal hash functions. [ABSTRACT FROM AUTHOR]

In [S. Safra, Proceedings of the 29th IEEE Symposium on Foundations of Computer Science, 1988, pp. 319-327] an exponential determinization procedure for Búchi automata was shown, yielding tight bounds for decision procedures of some logics (see [A. E. Emerson and C. Jutla, Proceedings of the 29th IEEE Symposium on Foundations of Computer Science, 1988, pp. 328-337; Safra (1988); S. Safra and M. Y. Vardi, Proceedings of the 21st ACM Symposium on Theory of Computing, 1989, pp. 127-137; and D. Kozen and J. Tiuryn, Logics of program, in Handbook of Theoretical Computer Science, Elsevier, Amsterdam, 1990, pp. 789-840]). In Safra and Vardi (1989) the complexity of determinization and complementation of ü-automata was further investigated, leaving as an open question the complexity of the determinization of a single class of ü-automata. For this class of ü-automata with strong fairness as an acceptance condition (Streett automata), Safra and Vardi (1989) managed to show an exponential complementation procedure; however, the blow-up of translating these automata—to any of the classes known to admit exponential determinization—is inherently exponential. This might suggest that the blow-up of the determinization of Streett automata is inherently doubly exponential. This paper shows an exponential determinization construction for Streett automata. In fact, the complexity of our construction is roughly the same as the complexity achieved in Safra (1988) for Búchi automata. Moreover, a simple observation extends this upper bound to the complementation problem. Since any ü-automaton that admits exponential determinization can be easily converted into a Streett automaton, we have obtained a single procedure that can be used for all of these conversions. Furthermore, this construction is optimal (up to a constant factor in the exponent) for all of these conversions. Our results imply that Streett automata (with strong fairness as an acceptance condition) can be used instead of Büchi automata (with the weaker acceptance condition) without any loss of efficiency. [ABSTRACT FROM AUTHOR]

This paper describes the construction of pedagogical environments in mathematics classes, centred on mathematical modelling and denominated ‘investigative scenarios’, which stimulate students to investigation, to formulation of problems and to political reflection, as well as the sharing of acquired knowledge with other persons in the community. The paper is based on the application of modelling as a teaching and learning strategy and on the pedagogical work with teenagers in an assisted freedom program. Both were accomplished in a scenario built with 10 volunteer students taking calculus in a Computer Engineering course in 2003. Among the main results we emphasise the academic maturing process for the student, how competent he gets in making models, accomplishing simulations, his perception of the relation between mathematical learning and everyday situations and political reflection about the results from working with modelling as much as about his participation in the community work. [ABSTRACT FROM AUTHOR]

In order to get undergraduates interested in mathematics, it is essential to involve them in its ‘discovery’. In this paper, we will explain how technology and the knowledge of lower dimensional calculus can be used to help them develop intuition leading to their discovering the first derivative rule in multivariable calculus. [ABSTRACT FROM AUTHOR]

This paper deals with the mathematical analysis of a model of urban dynamics, which was proposed by Miyata and Yamaguchi in the context of a region of Japan. The model is a complex system of first-order nonlinear ordinary differential equations. The study undertaken by Miyata and Yamaguchi is essentially computational, while an extensive study of the asymptotic behavior of the solutions is performed in this paper related to a detailed analysis of the qualitative properties of the system. [ABSTRACT FROM AUTHOR]

Various problems of electrical engineering lead to mathematical models being difference, differential or integral equations. In this paper some mathematical models in certain problems of electrical engineering are presented. Our considerations are restricted to the radiative heat transfer and density theory (Fredholm integral equations). Respecting time in current density problems we get integro-differential equations or generally Volterra-Fredholm integral equations (heat-conduction theory). The new numerical method for these equations is analysed. [ABSTRACT FROM AUTHOR]

A new incomplete data model, the trunsored model, in lifetime analysis is introduced. This model can be regarded as a unified model of the censored and truncated models. Using the model, we can not only estimate the ratio of the fragile population to the mixed fragile and durable populations, but also test a hypothesis that the ratio is equal to a prescribed value. A central point of the paper is that such a test can easily be realized through the newly introduced trunsored model, because it has been difficult to do such a hypothesis test under only the framework of censored and truncated models. Therefore, the relationship of the trunsored model to the censored and truncated models is clarified because the trunsored model unifies the censored and truncated models. The paper also shows how to obtain the estimates of the parameters in lifetime estimation, and corresponding confidence intervals for the fragile population. Typical examples applied to electronic board failures. and to breast cancer data, for lifetime estimation are demonstrated, and successfully worked using the trunsored model. [ABSTRACT FROM AUTHOR]

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems. [ABSTRACT FROM AUTHOR]

The paper reviews single-neuron learning rules for minor component analysis and suggests a novel minor component learning rule. In this rule, the weight vector length is self-stabilizing, i.e., moving towards unit length in each learning step. In simulations with low- and medium-dimensional data, the performance of the novel learning rule is compared with previously suggested rules. [ABSTRACT FROM AUTHOR]

Families of matrices smoothly depending on a vector of parameters are considered. Arnold [Russian Math. Surveys, 26 (1971), pp. 29–43] and Galin [Uspekhi Mat. Nauk, 27 (1972),pp. 241–242] have found and listed normal forms of families of complex and real matrices (miniversal deformations), to which any family of matrices can be transformed in the vicinity of a point in the parameter space by a change of basis, smoothly dependent on a vector of parameters, and by a smooth change of parameters. In this paper a constructive method of determining functions describing a change of basis and a change of parameters, transforming an arbitrary family to the miniversal deformation, is suggested. Derivatives of these functions with respect to parameters are determined from a recurrent procedure using derivatives of the functions of lower orders and derivatives of the family of matrices. Then the functions are found as Taylor series. Examples are given. The suggested method allows using efficiently miniversal deformations for investigation of different properties of matrix families. This is shown in the paper where tangent cones (linear approximations) to the stability domain at the singular boundary points are found. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finding minimal length tree networks on the unit sphere Φ of a given point set (V) where distance is measured along great circular arcs. The related problems of finding a Steiner Minimal Tree SMT (V) and of finding a Minimum Spanning Tree MST(V) are treated through a simplicial decomposition technique based on computing the Delaunay Triangulation DT (V) and the Voronoi Diagram VD(V) of the given point set. O (N log N) algorithms for computing DT(V), VD(V), and WST(V) as well as an O(N log N) heuristic for finding a sub-optimal SMT(V) solution are presented, together with experimental results for randomly distributed points on Φ. [ABSTRACT FROM AUTHOR]

Purchasing managers face a complex problem when determining order quantities for multiple items in the presence of quantity discounts and resource limitations. In this paper, the problem is formulated as a mathematical programming model. An efficient solution algorithm is developed utilizing the Lagrangian relaxation approach. Extensive computational experiments are performed and the results are presented. [ABSTRACT FROM AUTHOR]

The importance of mathematics in the context of the scientific and technological development of humanity is determined by the possibility of creating mathematical models of the objects studied under the different branches of Science and Technology. The arithmetisation process that took place during the nineteenth century consisted of the quest to discover a new mathematical reality in which the validity of logic would stand as something essential and central. Nevertheless, in contrast to this process, the development of mathematical analysis within a framework that largely involves intuition and geometry is a fact that cannot go unnoticed amongst the mathematics community, as we shall show in this paper through the research made by Bernhard Riemann on complex variables. [ABSTRACT FROM AUTHOR]

Cultural disappearance in the social order is one of the concerns in Indonesia nowadays, one of which is Sundanese culture. In addition, the crash of globalization also requires people to be inspired by learning many aspects away from their own culture. This paper aims at increasing the position of ethno mathematics learning in attractive the disposition modeling of mathematics while maintaining the traditional culture. This quantitative study applied the Rasch Wins Step Model to survey 90 elementary pre-service elementary teachers education students as the respondents in which they were grouped based on educational background, namely science or non-science, and Sundanese language ability background, and by Sundanese and non-Sundanese language, based on educational background, 59 respondents were the students of natural science class, and 31 respondents were not the students of natural science class and consisting of 42 Sundanese respondents and 48 non-Sundanese respondents. The data were gathered by means of questionnaires regarding mathematics modeling disposition. The consequences exposed that most students decided to increase mathematics modeling disposition with ethno mathematics learning because student curiosity increases the understanding of Sundanese culture in learning mathematics. The more ordinary science and Sundanese origin support ethno mathematics learning compared to non-science and non-Sundanese mathematics modeling disposition. Mathematical modeling activities will be more meaningful for students if they use culture. [ABSTRACT FROM AUTHOR]

A proper edge-coloring of a graph defines at each vertex the set of colors of its incident edges. This set is called the palette of the vertex. In this paper we are interested in the minimum number of palettes taken over all possible proper colorings of a graph. [ABSTRACT FROM AUTHOR]

The result stated in the title is proved, thereby disproving the result shown in a 1983 paper by B. A. Barnes (Theorem 4.1). [ABSTRACT FROM AUTHOR]

Estimators of parameters of an investigated object can be considered after some time as insufficiently precise. Therefore, an additional measurement must be realized. A model of a measurement, taking into account both the original results and the new ones, has a litle more complicated covariance matrix, since the variance components occur in it. How to deal with them is the aim of the paper. [ABSTRACT FROM AUTHOR]

Abstract: this paper gives them some properties. This paper firstly introduces rough logic, and proposes factorization of model based on rough logic, and proposes the optimal factorization of model, so one complex model could be factorized into several simple models, which are easy to be handled. this paper not only gives them some properties, but also analyze the time complexity of it. [Copyright &y& Elsevier]

Abstract: This paper firstly introduces rough logic, and proposes factorization of model based on rough logic, and proposes the optimal factorization of model, so one complex model could be factorized into several simple models, which are easy to be handled. this paper gives them somae properties. [Copyright &y& Elsevier]

In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs. [ABSTRACT FROM AUTHOR]

Minimal log discrepancies (mld's) are related not only to termination of log flips [Shokurov, Algebr. Geom. Metody 246: 328–351, (2004)] but also to the ascending chain condition (ACC) of some global invariants and invariants of singularities in the Log Minimal Model Program (LMMP). In this paper, we draw clear links between several central conjectures in the LMMP. More precisely, our main result states that the LMMP, the ACC conjecture for mld's and the boundedness of canonical Mori-Fano varieties in dimension ≦ d imply the following: the ACC conjecture for a-lc thresholds, in particular, for canonical and log canonical (lc) thresholds in dimension ≦ d; the ACC conjecture for lc thresholds in dimension ≦ d + 1; and termination of log flips in dimension ≦ d + 1 for effective lc pairs. In particular, when d = 3 we can drop the assumptions on LMMP and boundedness of canonical Mori-Fano varieties. [ABSTRACT FROM AUTHOR]

A Smarandache graphoidal tree (k, d)-cover of a graph G is a partition of edges of G into trees T1, T2, …, Tl such that ∣E(Ti) ∩ E(Tj)∣ ≤ k and ∣Ti∣ ≤ d for integers 1 ≤ i, j ≤ l. In this paper we investigate the garphoidal tree covering number γT (G), i.e., Smarandache graphoidal tree (0,∞)-cover of complete graphs, complete bipartite graphs and products of paths and cycles. In [5] M.F.Foregger, define a parameter z′(G) as the minimum number of subsets into which the vertex set of G can be partitioned so that each subset induces a tree. In this paper we also establish the relation z′ (G) ≤T(G). [ABSTRACT FROM AUTHOR]

We develop a family of new interior penalty discontinuous Galerkin methods for the Keller-Segel chemotaxis model. This model is described by a system of two nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction-diffusion equation for the chemoattractant concentration. It has been recently shown that the convective part of this system is of a mixed hyperbolic-elliptic-type, which may cause severe instabilities when the studied system is solved by straightforward numerical methods. Therefore, the first step in the derivation of our new methods is made by introducing the new variable for the gradient of the chemoattractant concentration and by reformulating the original Keller-Segel model in the form of a convection-diffusionreaction system with a hyperbolic convective part. We then design interior penalty discontinuous Galerkin methods for the rewritten Keller-Segel system. Our methods employ the central-upwind numerical fluxes, originally developed in the context of finite-volume methods for hyperbolic systems of conservation laws. In this paper, we consider Cartesian grids and prove error estimates for the proposed high-order discontinuous Galerkin methods. Our proof is valid for pre-blow-up times since we assume boundedness of the exact solution. We also show that the blow-up time of the exact solution is bounded from above by the blow-up time of our numerical solution. In the numerical tests presented below, we demonstrate that the obtained numerical solutions have no negative values and are oscillation-free, even though no slope-limiting technique has been implemented. [ABSTRACT FROM AUTHOR]

Judy and Motta developed a customizable electrodeposition process for fabrication of very small metal structures on a substrate. In this process, layers of metal of various shapes are placed on the substrate, then the substrate is inserted in an electroplating solution. Some of the metal layers have power applied to them, while the rest of the metal layers are not connected to the power initially. Metal ions in the plating solution start depositing on the powered layers and a surface grows from the powered layers. As the surface grows, it will touch metal layers that were initially unpowered, causing them to become powered and to start growing with the rest of the surface. The metal layers on the substrate are known as seed layer patterns, and different seed layer patterns can produce different shapes. This paper presents a mathematical model, a forward simulation method, and an inverse problem solution for the growth of a surface from a seed layer pattern. The model describes the surface evolution as uniform growth in the direction normal to the surface. This growth is simulated in two and three dimensions using the level set method. The inverse problem is to design a seed layer pattern that produces a desired surface shape. Some surface shapes are not attainable by any seed layer pattern. For smooth attainable shapes, we present a computational method that solves this inverse problem. [ABSTRACT FROM AUTHOR]

For 2 × 2 × K contingency tables, Tomizawa considered a Shannon entropy type measure to represent the degree of departure from a log-linear model of no three-factor interaction (the NOTFI model). This paper proposes a generalization of Tomizawa's measure for 2 × 2 × K tables. The measure proposed is expressed by using Patil-Taillie diversity index or Cressie-Read power-divergence. A special case of the proposed measure includes Tomizawa's measure. The proposed measure would be useful for comparing the degrees of departure from the NOTFI model in several tables. [ABSTRACT FROM AUTHOR]

Unique parametrizations of models are very important for parameter interpretation and consistency of estimators. In this paper we analyze the identifiability of a general class of finite mixtures of multinomial logits with varying and fixed effects, which includes the popular multinomial logit and conditional logit models. The application of the general identifiability conditions is demonstrated on several important special cases and relations to previously established results are discussed. The main results are illustrated with a simulation study using artificial data and a marketing dataset of brand choices. [ABSTRACT FROM AUTHOR]