Necessary Conditions For Existence Research Articles

A Multiplication Technique for the Factorization of Bivariate Quaternionic Polynomials

We consider bivariate polynomials over the skew field of quaternions, where the indeterminates commute with all coefficients and with each other. We analyze existence of univariate factorizations, that is, factorizations with univariate linear factors. A necessary condition for existence of univariate factorizations is factorization of the norm polynomial into a product of univariate polynomials. This condition is, however, not sufficient. Our central result states that univariate factorizations exist after multiplication with a suitable univariate real polynomial as long as the necessary factorization condition is fulfilled. We present an algorithm for computing this real polynomial and a corresponding univariate factorization. If a univariate factorization of the original polynomial exists, a suitable input of the algorithm produces a constant multiplication factor, thus giving an a posteriori condition for existence of univariate factorizations. Some factorizations obtained in this way are of interest in mechanism science. We present an example of a curious closed-loop mechanism with eight revolute joints.

THE IMPORTANCE OF THE ORGANIZATION OF ACCOUNTING AND CLASSIFICATION OF ACCOUNTING

The article considers the current state of methodological tools for the formation of financial statements, based on the interests of consumers of such reporting and the current state of the domestic economy. On the basis of the organization of accounting the necessary general theoretical provisions and methodology of formation of system of the accounting administrative reporting are defined, following which it will be possible to speak about existence of necessary conditions of formation of a qualitative information base for acceptance of administrative decisions. A description of the range of users, which allows to limit the various options for financial reporting, taking into account their real needs and interests. Depending on the specific features of the company and the content of financial statements, the justification of categories according to the content of information. The place and significance of financial reporting in the process of forming macroeconomic indicators and determining the directions of classification of financial statements based on the results of spectral analysis of information interests of users of accounting information at the local level and at the macro level of the state as a user of information. For business entities, financial statements are allocated, which reflect information on ordinary and extraordinary activities with the appropriate details. The degree of automation of the management and accounting system, which is divided into automated, partially automated accounting and manually compiled, is considered. It is noted that the considered areas of grouping of financial statements take into account the information interests of users of accounting information both at the local level of individual enterprises and at the state level as users of information in the formation of macroeconomic indicators, which will improve their quality and improve the range of indicators.

Dyakonov surface magnons and magnon polaritons

We predicted one Dyakonov surface magnon (DSM) and two Dyakonov magnon polaritons (DSMPs) localized at the antiferromagnet (AF)-air interface. Their concise dispersion equations and necessary conditions of existence were obtained. The DSM is the magnetostatic limit of the first DSMP, which are situated inside the AF reststrahlen frequency band. The second DSMP has no magnetostatic limit and lies outside the frequency band. The specifical frequency ranges occupied by the DSM and DSMPs were analytically found. The DSMPs are hybrid-polarization surface polaritons and the DSM is a hybrid-polarization surface magnetostatic mode. The first DSMP possesses large attenuation constants so that it is highly localized at the surface. Compared with it, the second DSMP exhibits relatively small attenuation constants. According to the features of polarization obtained for either DSMP, we used the TE and TM radiations incident on the AF surface to calculate attenuated total reflection (ATR) spectra, respectively. These ATR spectra not only further prove the existence of the DSMPs but also demonstrate their observability in experiment. However, the DSM should be detected by means of a light-scattering technique.

Derivatives of local times for some Gaussian fields II

Given a (2,d)-Gaussian field Z={Z(t,s)=XtH1−X˜sH2,s,t≥0},where XH1 and X˜H2 are independent d-dimensional centered Gaussian processes satisfying certain properties, we will give a necessary condition for existence of derivatives of the local time of Z at x∈Rd, this condition is also sufficient when XH1 and X˜H2 satisfy the local nondeterminism property.

On two-weight codes

We consider q-ary (linear and nonlinear) block codes with exactly two distances: d and d+δ. We derive necessary conditions for existence of such codes (similar to the known conditions in the projective case). In the linear (but not necessary projective) case, we prove that under certain conditions the existence of such linear 2-weight code with δ>1 implies the following equality of greatest common divisors: (d,q)=(δ,q). Upper bounds for the maximum cardinality of such codes are derived by linear programming and from few-distance spherical codes. Tables of lower and upper bounds for small q=2,3,4 and qn<50 are presented.

Stochastic integration with respect to cylindrical semimartingales

In this work we introduce a theory of stochastic integration with respect to general cylindrical semimartingales defined on a locally convex space $\Phi$. Our construction of the stochastic integral is based on the theory of tensor products of topological vector spaces and the property of good integrators of real-valued semimartingales. This theory is further developed in the case where $\Phi$ is a complete, barrelled, nuclear space, where we obtain a complete description of the class of integrands as $\Phi$-valued locally bounded and weakly predictable processes. Several other properties of the stochastic integral are proven, including a Riemann representation, a stochastic integration by parts formula and a stochastic Fubini theorem. Our theory is then applied to provide sufficient and necessary conditions for existence and uniqueness of solutions to linear stochastic evolution equations driven by semimartingale noise taking values in the strong dual $\Phi'$ of $\Phi$. In the last part of this article we apply our theory to define stochastic integrals with respect to a sequence of real-valued semimartingales.

Analysis of Dasein in Kim Alex’s Story

By retelling the story of Kim Alex, one of the Koryo Saram, based on the documentary film Kim Alex’s Place: Ansan-Tashkent by Kim Soyoung (aka Kim Jeong) and the fundamental ontology of Martin Heidegger, this article actualizes storytelling as a phenomenological method of existential understanding and reframes the structure of existential understanding intersubjectively, in which the Other is a necessary condition of existence and understanding.

Optimal control and cost-effectiveness analysis of taeniasis and cysticercosis in humans, pigs and cattle

Taeniasis and cysticercosis are neglected food-borne diseases that pose challenge to food safety, human health and livelihood of rural livestock farmers. In this paper, an optimal control problem for the dynamics and control of taeniasis and cysticercosis in humans, pigs and cattle with its cost-effectiveness analysis is presented and analysed to determine the optimal and cost-effective strategy for disease control. A combination of two or more time dependent controls involving vaccination of pigs and cattle, meat inspection, environmental hygiene and sanitation, and the treatment of humans who are infected with taeniasis is carried out to study their impacts on disease control. The Pontryagin’s maximum principle is adopted to find the necessary conditions for existence of the optimal controls. The Runge Kutta order four forward-backward sweep method is implemented to solve the optimal control problem. The incremental cost-effectiveness ratio (ICER) is applied to determine the most cost-effective strategy for disease control. The optimal control results indicate that the strategy which focus on the combination of all interventions or that exclude vaccination of pigs and cattle is the most effective optimal control strategy in disease control. However, cost-effectiveness analysis results show that a strategy which excludes vaccination of pigs and cattle is the most cost-effective strategy for disease control. Based on these results, we recommend that interventions which focus on meat inspection, treatment of humans who are infected with taeniasis and improvement in hygiene and sanitation should be considered to control the transmission of taeniasis and cysticercosis in humans, pigs and cattle at a minimal cost.

Optimal control of an avian influenza model with multiple time delays in state and control variables

In this paper, we consider an optimal control model governed by a class of delay differential equation, which describe the spread of avian influenza virus from the poultry to human. We take three control variables into the optimal control model, namely: slaughtering to the susceptible and infected poultry ( \begin{document}$ u_{1}(t) $\end{document} ), educational campaign to the susceptible human population ( \begin{document}$ u_{2}(t) $\end{document} ) and treatment to infected population ( \begin{document}$ u_{3}(t) $\end{document} ). The model involves two time delays that stand for the incubation periods of avian influenza virus in the infective poultry and human populations. We derive first order necessary conditions for existence of the optimal control and perform several numerical simulations. Numerical results show that different control strategies have different effects on controlling the outbreak of avian influenza. At the same time, we discuss the influence of time delays on objective function and conclude that the spread of avian influenza will slow down as the time delays increase.

Haar wavelet collocation approach for the solution of fractional order COVID-19 model using Caputo derivative

This article is devoted to study a compartmental mathematical model for the transmission dynamics of the novel Coronavirus-19 under Caputo fractional order derivative. By using fixed point theory of Schauder’s and Banach we establish some necessary conditions for existence of at least one solution to model under investigation and its uniqueness. After the existence a general numerical algorithm based on Haar collocation method is established to compute the approximate solution of the model. Using some real data we simulate the results for various fractional order using Matlab to reveal the transmission dynamics of the current disease due to Coronavirus-19 through graphs.

A magic rectangle set on Abelian groups and its application

A Γ-magic rectangle set MRSΓ(a,b;c) of order abc is a collection of c arrays (a×b) whose entries are elements of group Γ of order abc, each appearing once, with all row sums in every rectangle equal to a constant ω∈Γ and all column sums in every rectangle equal to a constant δ∈Γ.In this paper we prove that for {a,b}≠{2α,2k+1} where α and k>0 are some natural numbers, a Γ-magic rectangle set MRSΓ(a,b;c) exists if and only if a and b are both even or |Γ| is odd or Γ has more than one involution. We proved that there does not exist a Γ-magic rectangle set MRSΓ(2,2k+1;c) for any Abelian group Γ of order (4k+2)c. Moreover we obtain sufficient and necessary conditions for existence of a Γ-magic rectangle MRSΓ(a,b)=MRSΓ(a,b;1).This work will also be potentially useful for graph theorists who work in graph labeling. We apply the main result for construction of two group magic-type labelings for some families of graphs. In particular we give necessary and sufficient conditions for tKn,n to be Γ-magic.

Some Philosophical Problems of Studying Complex Systems in the Universe

Introduction. The paper deals with the philosophical problems of functioning of the most complex phenomena in the universe: creation of the universe, emergence of life and appearance of consciousness. The scientific timeliness of the research is determined by that unceasing interest to the origin of the universe and life in it. The most difficult problem is the origin of intelligence in the universe which is confirmed through the ongoing research in the SETI program. The scientific novelty of research is that the authors link three fundamental problems relates to the origins of complexity in the universe in a single intellectual cluster.Methodology and sources. The analysis is based on the issues in modern cosmology, astrobiology and anthropology treated in the context of complex systems and their radical sensitivity to the uncontrolled initial conditions. In particular, one implies the so called “fine-tuning” of the cosmological parameters necessary for the origin of life on the planet Earth. The hypothetical deviation of the numerical values of such parameters by, let say some per cents, would exclude the development of the biological systems. However the sphere of the necessary conditions for these parameters does not guarantee the fulfillment of the sufficient conditions for creation complexity and a possibility of life. Such conditions are not determined by the physical and biological context and make inevitable an appeal for their interpretation to philosophical ideas. The methodological foundation of this research is based in finding the boundaries of efficiency of the necessary conditions for emergence of complexity and attempts to provide in some cases an interpretation of the possible sufficient conditions.Results and discussion. It is shown that it is impossible to account on scientific grounds for the original conditions which launched creation of the universe, emergence of life and appearance of consciousness. Scientifically, one can formulate the necessary conditions for existence of life in the universe and hence the embodied consciousness, however it is beyond the reach of science to account for the sufficient conditions. One simple model of origin of life illustrating the dependence of its phenomenon on the uncontrolled sufficient conditions is proposed on the grounds of analogy with Bernard’s instability in complex systems. If one identifies such phenomena as existence of the universe, biological and intelligent life with the behavior in super-complex material systems, there still remains a fundamental problem in unpredictability and contingency of those “initial” conditions which predetermined the factual outcomes in evolution of these complex systems. In other words science faces a fundamental limitedness in describing the sufficient conditions (sufficient reason) for those forms of complexity in nature with which this article deals.Conclusion. A scientific description of the most complex phenomena such as the universe as a whole, biological and intelligent life demonstrate its limited scope as regards the sufficient conditions for their happening. In this sense an exhaustive understanding of these phenomena becomes fundamentally impossible, showing that science functions in the conditions of the positive uncertainty.

Stability Analysis and Optimal Control for Yellow Fever Model with Vertical Transmission.

In this study, a deterministic model for the transmission dynamics of yellow fever (YF) in a human–mosquito setting in the presence of control measures is constructed and rigorously analyzed. In addition to horizontal transmissions, vertical transmission within mosquito population is incorporated. Analysis of the mosquito-only component of the model shows that the reduced model has a mosquito-extinction equilibrium, which is globally-asymptotically stable whenever the basic offspring number (N_{0}) is less than unity. The vaccinated and type reproduction numbers of the full-model are computed. Condition for global-asymptotic stability of the disease-free equilibrium of the model when N_{0} > 1 is presented. It is shown that, fractional dosing of YF vaccine does not meet YF vaccination requirements. Optimal control theory is applied to the model to characterize the controls parameters. Using Pontryagin’s maximum principle and modified forward–backward sweep technique, the necessary conditions for existence of solutions to the optimal control problem is determined. Numerical simulations of the models to assess the effect of fractional vaccine dosing on the disease dynamics and global sensitivity analysis are presented.

Global Dynamics of a Planar Filippov System with Symmetry

Chen [2016a, 2016b] studied global dynamics of the Filippov systems [Formula: see text], respectively. To study the global dynamics of [Formula: see text] completely, since the dynamics of [Formula: see text] is very simple, we are only interested in the global dynamics of [Formula: see text] in this paper. Firstly, we use Briot–Bouquet transformations and normal sector methods to discuss these degenerate equilibria at infinity. Secondly, we discuss the number of limit cycles completely. Then, the sufficient and necessary conditions of existence of the heteroclinic loop are found. To estimate the upper bound of the heteroclinic loop bifurcation function on parameter space, a result on the amplitude of a unique limit cycle of a discontinuous Liénard system is given. Finally, the complete bifurcation diagram and all global phase portraits are presented. The global dynamic property of system [Formula: see text] is totally different from systems [Formula: see text].

On Lie algebras responsible for integrability of (1+1)-dimensional scalar evolution PDEs

Zero-curvature representations (ZCRs) are one of the main tools in the theory of integrable PDEs. In [13], for any (1+1)-dimensional scalar evolution equation E, we defined a family of Lie algebras F(E) which are responsible for all ZCRs of E in the following sense. Representations of the algebras F(E) classify all ZCRs of the equation E up to local gauge transformations. In [12] we showed that, using these algebras, one obtains necessary conditions for existence of a Bäcklund transformation between two given equations.In this paper we show that, using the algebras F(E), one obtains some necessary conditions for integrability of (1+1)-dimensional scalar evolution PDEs, where integrability is understood in the sense of soliton theory. Using these conditions, we prove non-integrability for some scalar evolution PDEs of order 5. Also, we prove a result announced in [13] on the structure of the algebras F(E) for certain classes of equations of orders 3, 5, 7, which include KdV, mKdV, Kaup–Kupershmidt, Sawada–Kotera type equations. Among the obtained algebras for equations considered in this paper and in [12], one finds infinite-dimensional Lie algebras of certain polynomial matrix-valued functions on affine algebraic curves of genus 1 and 0.

A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.

Continuous Partial Maps on Block Designs

This paper studies the properties of balanced incomplete block designs – the systems of k-element subsets (blocks) of some finite set of elements, such that every element is included in r blocks, and every pair of elements is included in λ blocks. The block designs were introduced for the planning of statistical experiments, and since then they have found lots of other uses. One can define a continuous partial map on a block design as a partial map for which the preimage of every block is either a block or an empty set. The paper lists the main known properties of continuous partial maps on block designs are listed. One of the important properties which, in particular, provides a necessary condition for existence of continuous partial maps on a given block design, is the homogeneous lemma: for a nonempty continuous map on a block design the number of the elements in a (nonempty) preimage of every element is fixed and equals to a number d, a divisor of the block size k. The dual homogeneous hypothesis conjectures that every block which is a preimage of some other block has to be a preimage of a fixed number of blocks. If this hypothesis holds, one would get a property for the block designs and the continuous maps on them, which is as important as the homogeneous lemma, and it would be able to build new block designs by taking continuous map images of other block designs. The main new result of this work is a counterexample to the dual homogeneous hypothesis built as a composite block design – block design whose set of blocks can be partitioned into groups, each one making a block design on the same element set. In the last section two necessary conditions for a block design to be composite are provided. Also a way of reduction of the search for a block designs with given parameters to the Boolean satisfiability problem and to the pseudo-Boolean satisfiability problem is given. The paper provides an explicit algorithm that builds a system of Boolean or pseudo-Boolean expressions equivalent to the problem of search for a block designs is provided. Finally, it demonstrates the results of application of existing solvers to the obtained problems.

A nonlinear Schrödinger equation for gravity waves slowly modulated by linear shear flow**Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFC1401404 and 2017YFA0604102) and the National Natural Science Foundation of China (Grant No. 41830533).

Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schrödinger equation (NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple-scale analysis method. The gravity waves are influenced by a linear shear flow, which is composed of a uniform flow and a shear flow with constant vorticity. The modulational instability (MI) of the NLSE is analyzed, and the region of the MI for gravity waves (the necessary condition for existence of freak waves) is identified. In this work, the uniform background flows along or against wave propagation are referred to as down-flow and up-flow, respectively. Uniform up-flow enhances the MI, whereas uniform down-flow reduces it. Positive vorticity enhances the MI, while negative vorticity reduces it. Hence, the influence of positive (negative) vorticity on MI can be balanced out by that of uniform down (up) flow. Furthermore, the Peregrine breather solution of the NLSE is applied to freak waves. Uniform up-flow increases the steepness of the free surface elevation, while uniform down-flow decreases it. Positive vorticity increases the steepness of the free surface elevation, whereas negative vorticity decreases it.

Existence of incomplete canonical Kirkman covering designs

For u,v positive integers with u≡v≡4(mod6), let ICKCD(u,v) denote a canonical Kirkman covering design of order u missing one of order v. In this paper, it is shown that the necessary condition for existence of an ICKCD (u,v), namely u≥3v+4, is sufficient with one definite exception, (u,v)=(16,4), and possible exceptions when v>76, v≡4 (mod 12) and u∈{3v+4,3v+10}.

Multiclass information flow propagation control under vehicle-to-vehicle communication environments

Most existing models for information flow propagation in a vehicle-to-vehicle (V2V) communications environment are descriptive. They lack capabilities to control information flow, which may preclude their ability to meet application needs, including the need to propagate different information types simultaneously to different target locations within corresponding time delay bounds. This study proposes a queuing-based modeling approach to control the propagation of information flow of multiple classes. Two control parameters associated with a vehicle, the number of communication servers and the mean communication service rate, are leveraged to control the propagation performance of different information classes. A two-layer model is developed to characterize the information flow propagation wave (IFPW) under the designed queuing strategy. The upper layer is formulated as integro-differential equations to characterize the spatiotemporal information dissemination due to V2V communication. The lower layer characterizes the traffic flow dynamics using the Lighthill–Whitham–Richards model. The analytical solution of the asymptotic density of informed vehicles and the necessary condition for existence of the IFPW are derived for homogeneous traffic conditions. Numerical experiments provide insights on the impact of the mean communication service rate on information spread and its spatial coverage. Further, a numerical solution method is developed to solve the two-layer model, which aids in estimating the impacts of the control parameters in the queuing strategy on the IFPW speed under homogenous and heterogeneous conditions. The proposed modeling approach enables controlling the propagation of information of different information classes to meet application needs, which can assist traffic managers to design effective and efficient traffic management and control strategies under V2V communications.