Asymptotic Existence Research Articles

Asymptotic existence theorem for formal power series solutions of singularly perturbed linear q-difference equations

Asymptotic existence theorem for formal power series solutions of singularly perturbed linear q-difference equations

Partition of ordered triples into uniform holey ordered designs

AbstractA large set is a partition of all ordered triples of a ‐set into disjoint ordered designs of order . In this paper, we generalize the large set with to the notion of , representing a partition of all ordered triples of a ‐set into disjoint uniform holely ordered designs s. We show that a exists if and only if and , except for . Moreover, we study the existence of a with every member having a kind of resolution. We show that a resolvable exists if and only if , , , with 27 possible exceptions. For almost resolvable s, we prove the asymptotic existence and present a few infinite families.

The similarity theory of free turbulent shear flows of viscoelastic fluids

A new theory is formulated for the description of the conformation state of the polymer chains in free turbulent shear flows of viscoelastic fluids. Using self-similarity arguments and new scaling relations for the turbulent flux of conformation tensor we show the existence of minimum and maximum solvent dissipation reduction asymptotes, and four different polymer deformation regimes. The similarities with the maximum drag reduction asymptote of turbulent pipe flow is discussed and new scaling laws are obtained for all components of the mean conformation tensor at each deformation regime. Analytical solutions for the self-similar transverse profiles of the conformation tensor components are also obtained, providing the complete solution for the mean flow problem at the far field. The analysis is developed for both planar jets and wakes and covers the two limits of shear flows, with large and small velocity differences, respectively. Comparisons of the new theoretical results with several direct numerical simulations employing the FENE-P rheological model show excellent agreement.

Asymptotic properties of GEE with diverging dimension of covariates

In this paper, for the generalized estimating equation (GEE) with diverging number of covariates, the asymptotic properties of GEE estimator are considered. Under the weaker assumption on the minimum eigenvalue of Fisher information matrix and some other regular conditions, we prove the asymptotic existence, consistency and asymptotic normality of the GEE estimator and the asymptotic distribution of the test statistics of linear combination of the unknown parameters. The results are illustrated by Monte-Carlo simulations.

Asymptotic existence theorem for formal solutions with singularities of nonlinear partial differential equations via multisummability

In this paper, we consider the summability of formal solutions with singularities (such as logarithmic singularities, functional power singularities, etc.) of nonlinear partial differential equations in the complex domain. The main result is as follows: when a formal solution with singularities is given, under appropriate assumptions related to the formal solution, the equation has a true solution that admits the given formal solution as an asymptotic expansion. The proof is done by constructing a new formal solution that is equivalent to the given formal solution in the asymptotic sense and is multisummable in a suitable direction. The assumptions are stated in terms of the Newton polygon associated with the given formal solution.

Asymptotic Regularity and Existence of Time-Dependent Attractors for Second-Order Undamped Evolution Equations with Memory

Our purpose in this article is to study the asymptotic behavior of undamped evolution equations with fading memory on time-dependent spaces. By means of the theory of processes on time-dependent spaces, asymptotic a priori estimate and the technique of operator decomposition and the existence and asymptotic regularity of time-dependent attractors are, respectively, established in the critical case. At the same time, we also obtain the asymptotic regularity of the solution.

On a High-Precision Method for Studying Attractors of Dynamical Systems and Systems of Explosive Type

The author of this article considers a numerical method that uses high-precision calculations to construct approximations to attractors of dynamical systems of chaotic type with a quadratic right-hand side, as well as to find the vertical asymptotes of solutions of systems of explosive type. A special case of such systems is the population explosion model. A theorem on the existence of asymptotes is proved. The extension of the numerical method for piecewise smooth systems is described using the Chua system as an example, as well as systems with hysteresis.

Dynamic System Analysis of Investment in Both Production and R&D with Time Delay

This paper, according to the process of capital return, establishes a differential dynamics model of investment with two time delays. When both time delays are zero, it is proved that the model is positively invariant, uniformly bounded, and globally asymptotically stable by using the comparison principle and Bendixson–Dulac theorem. When at least one time delay is not zero, according to Hopf bifurcation theorem, the conditions of local asymptotic stability and existence of periodic solution of investment model are obtained. By using the normal form theory and the center manifold theory, the discriminant formula of periodic solution property of investment model is given. Under the condition of controlled time delay, the model is numerically simulated to verify the correctness of relevant analytical conclusions. Therefore, the investment model describes the dynamic process and development trend of project investment quite closely.

USING COMPUTER TECHNOLOGIES TO INVESTIGATION AND CONSTRUCTION PLANAR CURVES ASYMPTOTES

Questions concerning the computer study of the existence of asymptotes of planar curves and their practical construction are considered. This need is due to routiness and laboriousness of manual computations and to automate the process. This problem especially concerns the case of an implicit equation of curves represented by high order polynomials. A modified version of the justification of the algorithm for constructing the asymptotes of a planar curves in the case of multiple roots of the leading term of such a polynomial is proposed. The algorithm is implemented as a computer program.

Almost eulerian compatible spanning circuits in edge-colored graphs

Let G be a (not necessarily properly) edge-colored graph. A compatible spanning circuit in G is a closed trail containing all vertices of G in which any two consecutively traversed edges have distinct colors. As two extremal cases, the existence of compatible (i.e., properly edge-colored) Hamilton cycles and compatible Euler tours have been studied extensively. More recently, sufficient conditions for the existence of compatible spanning circuits visiting each vertex v of G at least ⌊(d(v)−1)∕2⌋ times in graphs satisfying Ore-type degree conditions have been established. In this paper, we continue the research on sufficient conditions for the existence of compatible spanning circuits visiting each vertex at least a specified number of times. We respectively consider graphs satisfying Fan-type degree conditions, graphs with a high edge-connectivity, and the asymptotical existence of such compatible spanning circuits in random graphs.

On complementary dual multinegacirculant codes

Linear codes with complementary duals intersect with their duals trivially. Multinegacirculant codes that are complementary dual are characterized algebraically and some good codes are found in this family. Exact enumeration is performed for indices 2 and 3, whereas special choices of the co-index and base field size are needed for higher indices. Asymptotic existence results are derived for the special class of such codes that have co-index a power of two by means of Dickson polynomials. This shows that there are infinite families of complementary dual multinegacirculant codes with relative distance satisfying a modified Gilbert-Varshamov bound.

The asymptotic existence of frames with a pair of orthogonal frame resolutions

Motivated by the applications to generalized Howell designs and multiply constant-weight codes, we establish an asymptotic existence theorem for (k, λ)-frames of type gn with a pair of orthogonal frame resolutions via decompositions of edge-colored complete digraphs into prescribed edge-colored subgraphs.

On ergodic properties of operator nets on the predual of von neumann algebras

In this paper, we proved theorems which give the conditions that special operator nets on a predual of von Neumann algebras are strongly convergent under the Markov case. Moreover, we investigate asymptotic stability and existence of a lower-bound function for such nets.

Long quasi-polycyclic <inline-formula><tex-math id="M1">\begin{document}$t-$\end{document}</tex-math></inline-formula> CIS codes

We study complementary information set codes of length $tn$ and dimension $n$ of order $t$ called ($t-$CIS code for short). Quasi-cyclic (QC) and quasi-twisted (QT) $t$-CIS codes are enumerated by using their concatenated structure. Asymptotic existence results are derived for one-generator and fixed co-index QC and QT codes depending on Artin's primitive root conjecture. This shows that there are infinite families of rate $1/t$ long QC and QT $t$-CIS codes with relative distance satisfying a modified Varshamov-Gilbert bound. Similar results are defined for the new and more general class of quasi-polycyclic codes introduced recently by Berger and Amrani.

Constructions for orthogonal designs using signed group orthogonal designs

Craigen introduced and studied signed group Hadamard matrices extensively and eventually provided an asymptotic existence result for Hadamard matrices. Following his lead, Ghaderpour introduced signed group orthogonal designs and showed an asymptotic existence result for orthogonal designs and consequently Hadamard matrices. In this paper, we construct some interesting families of orthogonal designs using signed group orthogonal designs to show the capability of signed group orthogonal designs in generation of different types of orthogonal designs.

Asymptotic existence of fair divisions for groups

The problem of dividing resources fairly occurs in many practical situations and is therefore an important topic of study in economics. In this paper, we investigate envy-free divisions in the setting where there are multiple players in each interested party. While all players in a party share the same set of resources, each player has her own preferences. Under additive valuations drawn randomly from probability distributions, we show that when all groups contain an equal number of players, a welfare-maximizing allocation is likely to be envy-free if the number of items exceeds the total number of players by a logarithmic factor. On the other hand, an envy-free allocation is unlikely to exist if the number of items is less than the total number of players. In addition, we show that a simple truthful mechanism, namely the random assignment mechanism, yields an allocation that satisfies the weaker notion of approximate envy-freeness with high probability.

Improving the Existence Bounds for Grid-Block Difference Families

In this paper, by employing Weil's Theorem on multiplicative character sums, an intermediate algebraic consequence on the existence bound of an element satisfying certain cyclotomic conditions in a finite field is proposed. In many cases, this approach improves the bound due to Buratti and Pasotti (Finite Fields Appl 15(3), 332---344, 2009), which can be widely used for showing the asymptotic existence of combinatorial designs with point-regular automorphisms. Moreover, this approach is applied to improving the existence bound for grid-block difference families, which can be regarded as generalizations of difference families.

THEORETICAL ANALYSIS OF SOCIAL ASSISTANCE POLICY

This paper examines the influence of social assistance program to the needy layers of the productive population. The analysis was conducted using a modified model of employee behavior – in a coordinate system « labor – consumption» («L – C»). The existence of asymptotes of the modified indifference curves are shown. The budget line is drawn with the fundamental psychological law Keynes. The influence of social assistance program is considered separately for «recipients» and «donors». A conclusion is grounded about ambiguous influence of the social program on these two groups of employees. Namely, in consequence of the introduction of social assistance program, low-income employees reduce their labor efforts. High-income employees are forced to reduce consumption. The synthetic model which combine the modified indifference curves and the production function as a limitation was used. On the basis of this model the macroeconomic consequences and limitations of social assistance program are considered

New Bounds and Constructions for Multiply Constant-Weight Codes

Multiply constant-weight codes (MCWCs) were introduced recently to improve the reliability of certain physically unclonable function response. In this paper, the bounds of MCWCs and the constructions of optimal MCWCs are studied. First, we derive three different types of upper bounds which improve the Johnson-type bounds given by Chee et al. for some parameters. The asymptotic lower bound of MCWCs is also examined. Then, we obtain the asymptotic existence of two classes of optimal MCWCs, which shows that the Johnson-type bounds for MCWCs with distances $2\sum _{i=1}^{m}w_{i}-2$ or $2mw-2w$ are asymptotically exact. Finally, we construct a class of optimal MCWCs with total weight four and distance six by establishing the connection between such MCWCs and a new kind of combinatorial structures. As a consequence, the maximum sizes of MCWCs with total weight less than or equal to four are determined almost completely.

Asymptotic existence of proportionally fair allocations

Fair division has long been an important problem in the economics literature. In this note, we consider the existence of proportionally fair allocations of indivisible goods, i.e., allocations of indivisible goods in which every agent gets at least her proportionally fair share according to her own utility function. We show that when utilities are additive and utilities for individual goods are drawn independently at random from a distribution, proportionally fair allocations exist with high probability if the number of goods is a multiple of the number of agents or if the number of goods grows asymptotically faster than the number of agents.