Closure Properties Research Articles

A CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY KOMATU INTEGRAL OPERATOR

In this paper, we introduce a subclasses of analytic functions with negative coefficients defined by Komatu integral operator. We obtain the coefficient bounds, growth distortion properties, extreme points and radii of starlikeness and convexity and close-to-convexity for functions belonging to the class $TS_{a, \delta} ^{~ k} (\vartheta ,\hbar ,\ell )$. Furthermore, we obtained modified Hardamard product, closure properties for this class.

On a Set of Generalized Janowski-Type Starlike Functions Connected With Mathieu-Type Series and Opoola Differential Operator

The study carried out in this paper is on a set of analytic-univalent functions whose definition is connected with the applications of the normalized Mathieu-type series, Opoola differential operator, Oyekan-Swamy-Opoola operator and Janowski-type starlike functions. More so, the techniques of convolution and subordination are embraced in the definition of our set of functions. Some of our investigations include the coefficient inequality, radii problems, growth, distortion, closure and inclusion properties.

Margin‐closed vector autoregressive time series models

Conditions are obtained for a Gaussian vector autoregressive time series of order , VAR(), to have univariate margins that are autoregressive of order or lower‐dimensional margins that are also VAR(). This can lead to ‐dimensional VAR() models that are closed with respect to a given partition of by specifying marginal serial dependence and some cross‐sectional dependence parameters. The special closure property allows one to fit the subprocesses of multi‐variate time series before assembling them by fitting the dependence structure between the subprocesses. We revisit the use of the Gaussian copula of the stationary joint distribution of observations in the VAR() process with non‐Gaussian univariate margins but under the constraint of closure under margins. This construction allows more flexibility in handling higher‐dimensional time series and a multi‐stage estimation procedure can be used. The proposed class of models is applied to a macro‐economic data set and compared with the relevant benchmark models.

A Theory of Formal Choreographic Languages

We introduce a meta-model based on formal languages, dubbed formal choreographic languages, to study message-passing systems. Our framework allows us to generalise standard constructions from the literature and to compare them. In particular, we consider notions such as global view, local view, and projections from the former to the latter. The correctness of local views projected from global views is characterised in terms of a closure property. We consider a number of communication properties -- such as (dead)lock-freedom -- and give conditions on formal choreographic languages to guarantee them. Finally, we show how formal choreographic languages can capture existing formalisms; specifically we consider communicating finite-state machines, choreography automata, and multiparty session types. Notably, formal choreographic languages, differently from most approaches in the literature, can naturally model systems exhibiting non-regular behaviour.

Array generating fuzzy petri nets and rectangular picture languages

A two dimensional language is a collection of two dimensional words, which are rectangular array of symbols made up of finite alphabets. Fuzzy Petri nets are the generalization of classical Petri nets designed to deal with imprecise and ambiguous data which usually occurs in knowledge based systems, image processing, etc. They have been widely used to represent fuzzy production rules and fuzzy rule-based reasoning. In this paper, a new model called array token fuzzy Petri net to generate two dimensional fuzzy regular languages has been introduced. Array token fuzzy Petri nets are used to deal with impreciseness and uncertainties occurring in two dimensional regular languages. Furthermore, proved that for every two dimensional fuzzy regular grammar there exists an array token fuzzy Petri net that generates the same two dimensional fuzzy regular language and also establish some closure properties of the languages generated by array token fuzzy Petri net.

Excitonic insulator to superconductor phase transition in ultra-compressed helium

Helium, the second most abundant element in the universe, exhibits an extremely large electronic band gap of about 20 eV at ambient pressures. While the metallization pressure of helium has been accurately determined, thus far little attention has been paid to the specific mechanisms driving the band-gap closure and electronic properties of this quantum crystal in the terapascal regime (1 TPa = 10 Mbar). Here, we employ density functional theory and many-body perturbation calculations to fill up this knowledge gap. It is found that prior to reaching metallicity helium becomes an excitonic insulator (EI), an exotic state of matter in which electrostatically bound electron-hole pairs may form spontaneously. Furthermore, we predict metallic helium to be a superconductor with a critical temperature of ≈ 20 K just above its metallization pressure and of ≈ 70 K at 100 TPa. These unforeseen phenomena may be critical for improving our fundamental understanding and modeling of celestial bodies.

On regular copying languages

This paper proposes a formal model of regular languages enriched with unbounded copying. We augment finite-state machinery with the ability to recognize copied strings by adding an unbounded memory buffer with a restricted form of first-in-first-out storage. The newly introduced computational device, finite-state buffered machines (FS-BMs), characterizes the class of regular languages and languages de-rived from them through a primitive copying operation. We name this language class regular copying languages (RCLs). We prove a pumping lemma and examine the closure properties of this language class. As suggested by previous literature (Gazdar and Pullum 1985, p.278), regular copying languages should approach the correct characteriza-tion of natural language word sets.

Optimization of Generalized Certainty Equivalents on the Finite Horizon

This paper addresses some open issues in optimization of generic certainty equivalents. Such equivalents have been modelled using increasing functionals of the discounted sums of the per-stage unbounded-above cost or reward functions defined on the paths of the underlying controlled Markov chain on general state spaces which models the random dynamics of the system. Examples of such functionals include logarithmic and power utilities as well as the robust Risk-Sensitive preferences among others. The critical results that were obtained were the solutions of this problem for generic unbounded-above per-stage cost minimization and for per stage reward maximization, both satisfying a w-growth (hence unbounded) condition in the nite horizon setup. In the process, we establish certain nontrivial closure properties of the dynamic programming operators. In addition, we provide a real-life example from Portfolio Consumption.

On Tsirelson pairs of C*-algebras

We introduce the notion of a Tsirelson pair of C*-algebras, which is a pair of C*-algebras for which the space of quantum strategies obtained by using states on the minimal tensor product of the pair is dense in the space of quantum strategies obtained by using states on the maximal tensor product. We exhibit a number of examples of such pairs that are “nontrivial” in the sense that the minimal tensor product and the maximal tensor product of the pair are not isomorphic. For example, we prove that any pair containing a C*-algebra with Kirchberg’s QWEP property is a Tsirelson pair. We then introduce the notion of a C*-algebra with the Tsirelson property (TP) and establish a number of closure properties for this class. We also show that the class of C*-algebras with the TP forms an elementary class (in the sense of model theory), but that this class does not admit an effective axiomatization.

Syntax checking either way

We consider parsers of deterministic context-free languages and study the sizes of their syntax checking components. More precisely, we allow the input processing from left to right or, alternatively, from right to left, whatever is best for the given language. As practical examples, we establish an infinite sequence of deterministic context-free languages Lk, for k≥1, such that there is an exponential size trade-off between a deterministic pushdown automaton that reads its input from right to left and another one that reads its input from left to right. Concerning the constructibility of such a parser out of a given deterministic context-free language, it is shown that it is undecidable whether the reversal of a given deterministic context-free language is again deterministic context free. Related to decidability questions, it turns out that the size trade-offs between deterministic pushdown automata that represent the reversals of their accepted languages and deterministic pushdown automata that represent their accepted languages are non-recursive. That is, one can choose an arbitrarily large recursive function ϱ, but the gain in economy of description eventually exceeds ϱ when changing from the former system to the latter. Furthermore, we study the expressive capacity of the family of languages whose reversals are deterministic context free. Finally, we turn to the family of deterministic context-free languages whose reversals are also deterministic context free and collect several of their closure properties.

A generalization of the increasing generalized failure rate unimodality condition

In this paper, we study unimodality conditions for distributions that describe markets with stochastic demand. Such conditions naturally emerge in the analysis of game-theoretic models of market competition (Cournot games) and supply chain coordination (Stackelberg games). We express the price elasticity of expected demand in terms of the mean residual life (MRL) function of the demand distribution and characterize optimal prices or equivalently, points of unitary elasticity, as fixed points of the MRL function. This leads to economic interpretable conditions on the demand distribution under which such fixed points exist and are unique. We find that markets with increasing price elasticity of expected demand that eventually become elastic correspond to distributions with decreasing generalized mean residual life (DGMRL) and finite second moment. DGMRL distributions strictly generalize the widely used increasing generalized failure rate (IGFR) distributions. We further elaborate on the relationship of the two classes, link their limiting behavior at infinity and examine moment and closure properties of DGMRL distributions that are important in economic applications. The DGMRL unimodality condition is useful in the analysis of optimal decisions under uncertainty in settings that are not covered by the widely-used IGFR condition; thus, it can be of broader interest to the game-theory and operations research literature.

Fresh function spectra

In this paper, we investigate the fresh function spectrum of forcing notions, where a new function on an ordinal is called fresh if all its initial segments are in the ground model. We determine the fresh function spectrum of several forcing notions and discuss the difference between fresh functions and fresh subsets. Furthermore, we consider the question which sets are realizable as the fresh function spectrum of a homogeneous forcing. We show that under GCH all sets with a certain closure property are realizable, while consistently there are sets which are not realizable.

Truncated Moments for Heavy-Tailed and Related Distribution Classes

Suppose that ξ+ is the positive part of a random variable defined on the probability space (Ω,F,P) with the distribution function Fξ. When the moment Eξ+p of order p>0 is finite, then the truncated moment F¯ξ,p(x)=min1,Eξp1I{ξ>x}, defined for all x⩾0, is the survival function or, in other words, the distribution tail of the distribution function Fξ,p. In this paper, we examine which regularity properties transfer from the distribution function Fξ to the distribution function Fξ,p and which properties transfer from the function Fξ,p to the function Fξ. The construction of the distribution function Fξ,p describes the truncated moment transformation of the initial distribution function Fξ. Our results show that the subclasses of heavy-tailed distributions, such as regularly varying, dominatedly varying, consistently varying and long-tailed distribution classes, are closed under this truncated moment transformation. We also show that exponential-like-tailed and generalized long-tailed distribution classes, which contain both heavy- and light-tailed distributions, are also closed under the truncated moment transformation. On the other hand, we demonstrate that regularly varying and exponential-like-tailed distribution classes also admit inverse transformation closures, i.e., from the condition that Fξ,p belongs to one of these classes, it follows that Fξ also belongs to the corresponding class. In general, the obtained results complement the known closure properties of distribution regularity classes.

Closure Properties of Subregular Languages Under Operations

A class of languages is closed under a given operation if the resulting language belongs to this class whenever the operands belong to it. We examine the closure properties of various subclasses of regular languages under basic operations of intersection, union, concatenation and power, positive closure and star, reversal, and complementation. We consider the following classes: definite languages and their variants (left ideal, finitely generated left ideal, symmetric definite, generalized definite and combinational), two-sided comets and their variants comets and stars, and the classes of singleton, finite, ordered, star-free, and power-separating languages. We also give an overview about subclasses of convex languages (classes of ideal, free, and closed languages), union-free languages, and group languages. We summarize some inclusion relations between these classes. Subsequently, for all pairs of a class and an operation, we provide an answer whether this class is closed under this operation or not.

Parameterised Counting in Logspace

Logarithmic space-bounded complexity classes such as textbf{L} and textbf{NL} play a central role in space-bounded computation. The study of counting versions of these complexity classes have lead to several interesting insights into the structure of computational problems such as computing the determinant and counting paths in directed acyclic graphs. Though parameterised complexity theory was initiated roughly three decades ago by Downey and Fellows, a satisfactory study of parameterised logarithmic space-bounded computation was developed only in the last decade by Elberfeld, Stockhusen and Tantau (IPEC 2013, Algorithmica 2015). In this paper, we introduce a new framework for parameterised counting in logspace, inspired by the parameterised space-bounded models developed by Elberfeld, Stockhusen and Tantau. They defined the operators textbf{para}_{textbf{W}} and textbf{para}_beta for parameterised space complexity classes by allowing bounded nondeterminism with multiple-read and read-once access, respectively. Using these operators, they characterised the parameterised complexity of natural problems on graphs. In the spirit of the operators textbf{para}_{textbf{W}} and textbf{para}_beta by Stockhusen and Tantau, we introduce variants based on tail-nondeterminism, textbf{para}_{{textbf{W}}[1]} and textbf{para}_{beta {textbf{tail}}}. Then, we consider counting versions of all four operators and apply them to the class textbf{L} . We obtain several natural complete problems for the resulting classes: counting of paths in digraphs, counting first-order models for formulas, and counting graph homomorphisms. Furthermore, we show that the complexity of a parameterised variant of the determinant function for (0, 1)-matrices is #textbf{para}_{beta {textbf{tail}}}textbf{L} -hard and can be written as the difference of two functions in #textbf{para}_{beta {textbf{tail}}}textbf{L} . These problems exhibit the richness of the introduced counting classes. Our results further indicate interesting structural characteristics of these classes. For example, we show that the closure of #textbf{para}_{beta {textbf{tail}}}textbf{L} under parameterised logspace parsimonious reductions coincides with #textbf{para}_beta textbf{L} . In other words, in the setting of read-once access to nondeterministic bits, tail-nondeterminism coincides with unbounded nondeterminism modulo parameterised reductions. Initiating the study of closure properties of these parameterised logspace counting classes, we show that all introduced classes are closed under addition and multiplication, and those without tail-nondeterminism are closed under parameterised logspace parsimonious reductions. Finally, we want to emphasise the significance of this topic by providing a promising outlook highlighting several open problems and directions for further research.

Pascu-Rønning Type Meromorphic Functions Based on Sălăgean-Erdély–Kober Operator

In the present investigation, we introduce a new class of meromorphic functions defined in the punctured unit disk Δ*:={ϑ∈C:0<|ϑ|<1} by making use of the Erdély–Kober operator Iς,ϱτ,κ which unifies well-known classes of the meromorphic uniformly convex function with positive coefficients. Coefficient inequalities, growth and distortion inequalities, in addition to closure properties are acquired. We also set up a few outcomes concerning convolution and the partial sums of meromorphic functions in this new class. We additionally state some new subclasses and its characteristic houses through specializing the parameters that are new and no longer studied in association with the Erdély–Kober operator thus far.

Mining periodic high-utility itemsets with both positive and negative utilities

Mining high-utility patterns in databases containing items with both positive and negative profits is useful in market basket databases, since negative profits are common in the real world. Obviously, in the market basket database, patterns with stable long-term profits have more meaning. The discovery of itemsets with a consistent high frequency is known as periodic frequent pattern mining. Therefore, mining periodic high-utility patterns in a database containing items with both positive and negative profits is an interesting and useful task. However, this task has two main challenges. First, the utility measure does not have the download closure property. Second, the huge search space needs to be pruned more effectively. In this paper, we propose a vertical data structure-based algorithm called PHMN to discover periodic high-utility patterns (PHUPs) or itemsets in a transaction database with both positive and negative utilities. To be more efficient, we propose a new upper bound to prune the search space and an improved algorithm to discover the PHUPs. Finally, experiments are conducted to verify the effectiveness and efficiency of algorithms.

One-step closure, weak one-step closure and meet continuity

This paper studies the weak one-step closure and one-step closure properties concerning the structure of Scott closures. We deduce that every quasicontinuous domain has weak one-step closure and show that a quasicontinuous poset need not have weak one-step closure. We also constructed a non-continuous poset with one-step closure, which gives a negative answer to an open problem posed by Zou et al.. Finally, we investigate the relationship between weak one-step closure property and one-step closure property and prove that a poset has one-step closure if and only if it is meet continuous and has weak one-step closure.

CRISIS PREVENTION: THE IMPACT OF PROJECT MANAGEMENT, PLANNING AND MARKETING RESEARCH

The article is devoted to the justification of the need to take into account the influence of project management, planning and marketing research when developing the theory of crisis based on the theory of systems, the transdisciplinary approach, the law of structural harmony of systems, the logical-structural approach in the management of projects and programs. The quality of management decision-making at all levels of the hierarchy depends on the analysis of the external and internal environment. The tool of analysis is marketing research. An attempt was made to substantiate the hypothesis regarding the need to implement a hierarchical planning system to ensure dynamic development and counter the spread of crisis phenomena and the evolution of the crisis. Each integral complex open system, schematically or enlarged, has three basic components: input - contour of operational closure - output. Operational closeness is a system property that affects the behavior of the system as a result of the interaction of the network of circuit processes, the action of these processes in the circuit forms the emergence of super-properties or the effect of emergence, or the synergistic effect. The property of operational closure that is the most important and interacts with the properties of self-organization and selfharmonization. Together, these three properties ensure the stability of the system and its viability to changes and various kinds of bifurcations for the period between these bifurcations (crisis phenomena) and changes in the state of the system and its transition to a new level. In such periods, there is a need to measure and assess the state of the system, which is practically impossible to do with the help of conventional indicators and indicators. Task of scientific ground of mathematical parameters the contour of economic security and development of model of the planning system which it will be possibly to balance with the requirements of market acquires the special actuality at the terms of the state of singular vertical line of crises. Singularity is instrument of evolution of crisis: system crisis – structural crisis – polycrisis with terrible consequences for socioeconomic, etc. systems of any state. Modern researches in relation to development of effective model of counteraction a crisis, it follows to carry out on the basis of transdisciplinary approach. It’s help to exams the level of general acts of shaping, for example – to self-shaping of cycle, which is perspective direction of development of theory of management of complex systems.

Weighted Multiple Context-Free Grammars

Multiple context-free grammar (MCFG) is an extension of context-free grammar (CFG), which generates tuples of words. The expressive power of MCFG is between CFG and context-sensitive grammar while MCFG inherits good properties of CFG. In this paper, we introduce weighted multiple context-free grammar (WMCFG) as a quantitative extension of MCFG. Then we investigate properties of WMCFG such as polynomial-time computability of basic problems, its closure property and expressive power.