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Данная статья является апробацией авторской методики инверсивного семиотического анализа и исследованием с помощью данной методики конкретного художественного текста - романа Ф. Сологуба «Мелкий бес». В основе инверсивного семиотического анализа лежит представление об инверсии - особом типе отношений в иерархических структурах, при которых низший элемент обретает главенствующие свойства, формально оставаясь на прежней, подчиненной позиции. Проведенные исследования позволили выявить в тексте романа различные уровни инверсии: в поведении и описании героев, изображении социальных и психических процессов. Это позволило сделать вывод о том, что инвертивность семиотических планов формирует семиотический код текста. This article is an approbation of the author's method of inverse semiotic analysis and research with the help of this method of a specific literary text - the novel by F. Sologub «The Little Demon». Inverse semiotic analysis is based on the concept of inversion - a special type of relationship in hierarchical structures in which the lower element acquires dominant properties, formally remaining in the same subordinate position. The studies carried out allowed us to identify different levels of inversion in the text of the novel: in the behavior and description of the characters, in the depiction of social and mental processes. This made it possible to conclude that the inversion of semiotic plans forms the semiotic code of the text.

In this paper, a new method of state stability, transition and tracking control for dynamics system based on model prediction and inversion is introduced. The estimation of system state bias in the future is obtained by model prediction. According to the dynamics evolution law of the controlled object, the control command to eliminate the future deviation is obtained by dynamics inversion. The compensation control is designed for the current and historical state deviations, and a state control method based on dynamics model of the controlled object is constructed. This method can be widely applied to various forms of control, and can better realize the state transition, tracking and stability control of dynamics system under the time constraint. The controller can be self-organized according to the model of the controlled object, and the parameters of the controller can be adjusted adaptively. It has good robustness to load/disturbance and deviations of model parameter, state measurement and control execution. The characteristics of this method are discussed, a simulation of rocket attitude control is given and the future research focus of this method is prospected.

Though generating a sequence of pseudorandom numbers by linear methods (Lehmer generator) displays acceptable behavior under some conditions of the parameters, it also has undesirable features, which makes the sequence unusable for various stochastic simulations. An extension which showed promise for such applications is a generator obtained by using a first-order recurrence based upon the inversive modulo a prime or a prime power, called inversive congruential generator (ICG). A lot of work has been dedicated to investigate the periods (under some conditions of the parameters), the lattice test passing, discrepancy and other statistical properties of such a generator. Here, we propose a new method, which we call hybrid inversive congruential generator (HICG), based upon a second order recurrence using the inversive modulo M, a power of 2. We investigate the period of this pseudorandom numbers generator (PRNG) and give necessary and sufficient conditions for our PRNG to have periods M (thereby doubling the period of the classical ICG) and M/2 (matching the one of the ICG). Moreover, we show that the lattice test complexity for a binary sequence associated to (a full period) HICG is precisely M/2.

In this paper we present a method of characteristic sets for inversive difference polynomials and apply it to the analysis of systems of quasi-linear algebraic difference equations. We describe characteristic sets and compute difference dimension polynomials associated with some such systems. Then we apply our results to the comparative analysis of difference schemes for some PDEs from the point of view of their Einstein's strength. In particular, we determine the Einstein's strength of standard finite-difference schemes for the Murray, Burgers and some other reaction-diffusion equations., Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:1803.03830

We establish some inequalities for self-inversive rational functions with prescribed poles in the sup-norm on the unit circle in the complex plane. Generalizations of polynomial inequalities of Malik and O?Hara and Rodriguez are obtained for such rational functions

We present a method of Grobner bases with respect to several term orderings and use it to obtain new results on multivariate dimension polynomials of inversive difference modules. Then we use the difference structure of the module of Kahler differentials associated with a finitely generated inversive difference field extension of a given difference transcendence degree to describe the form of a multivariate difference dimension polynomial of the extension.

We study some special types of bands of E-inversive unipotent semigroups. It has been proved that in any R-semigroup S, which is a band of E-inversive unipotent semigroups, the set of its regular elements is a retract of S. Also, some characterizations of E-inversive rectangular bands of unipotent semigroups are given. This theorem extends nearly 40-old results from the theory of epigroups. In fact, a more general result is valid in some special subclass of the class of E-inversive semigroups; this result seems to be (partially) new for all epigroups.

Circular tubes having preformed feature which induce inversion type of deformation under axial loading are referred to as invertubes. Invertubes are used as impact energy absorbers due to their peculiar inversive mode of deformation upon axial crash-impact and exhibit less initial peak force with nearly 100% stroke and crush force efficiencies. But restrictions on the combination of invertube's geometric profile and material's ductility significantly limit the specific energy absorption (SEA), a critical crash performance parameter that influences the selection of an energy absorbing (EA) structure. Therefore, this paper proposes invertubes with multi-material structural configurations to achieve higher SEA. Initially, a base monolithic configuration of invertube made of SS304 has been studied numerically and validated by experiment. Subsequently, a few invertube configurations have been proposed over this base configuration by combination of different metals and composites. Relative merits and limitations of each variant (configuration) have been discussed in detail with a specific relevance to enhancement in SEA.

The standard cardioid is the set of points in the complex plane formed by reflecting the point 1 in every tangent to the unit circle. These points constitute a simple closed curve that is the bound...

We verify the infinitesimal inversive rigidity of almost all triangulated circle polyhedra in the Euclidean plane $${\mathbb {E}}^{2}$$ , as well as the infinitesimal inversive rigidity of tangency circle packings on the 2-sphere $${\mathbb {S}}^{2}$$ . From this the rigidity of almost all triangulated circle polyhedra follows. The proof adapts Gluck’s proof (Geometric Topology, volume 238 of Lecture Notes in Mathematics, pp 225–239, 1975) of the rigidity of almost all Euclidean polyhedra to the setting of circle polyhedra, where inversive distances replace Euclidean distances and Mobius transformations replace rigid Euclidean motions.

Inverting the vertices of elliptic billiard N-periodics with respect to a circle centered on one focus yields a new "focus-inversive" family inscribed in Pascal's Lima\c{c}on. The following are some of its surprising invariants: (i) perimeter, (ii) sum of cosines, and (iii) sum of distances from inversion center (the focus) to vertices. We prove these for the N=3 case, showing that this family (a) has a stationary Gergonne point, (b) is a 3-periodic family of a second, rigidly moving elliptic billiard, and (c) the loci of incenter, barycenter, circumcenter, orthocenter, nine-point center, and a great many other triangle centers are circles., Comment: 15 pages, 10 figures, 2 tables, 9 video links

In this short paper, we study the capacity-constrained vehicle routing problem (CVRP) and its solution by randomized Monte Carlo methods. For solving CVRP we use some pseudorandom number generators commonly used in practice. We use linear, multiple-recursive, inversive, and explicit inversive congruential generators and obtain random numbers from each to provide a route for CVRP. Then we compare the performance of pseudorandom number generators with respect to the total time the random route takes. We also constructed an open-source library github.com/iedmrc/binary-cws-mcs on solving CVRP by Monte-Carlo based heuristic methods., Comment: 6 pages, 2nd International Conference on Electrical, Communication and Computer Engineering (ICECCE), 12-13 June 2020, Istanbul, Turkey

Let K be an inversive difference-differential field and L a (not necessarily inversive) finitely generated difference-differential field extension of K. We consider the natural filtration of the extension L/K associated with a finite system \(\eta \) of its difference-differential generators and prove that for any intermediate difference-differential field F, the transcendence degrees of the components of the induced filtration of F are expressed by a certain numerical polynomial \(\chi _{K, F,\eta }(t)\). This polynomial is closely connected with the dimension Hilbert-type polynomial of a submodule of the module of Kahler differentials \(\varOmega _{L^{*}|K}\) where \(L^{*}\) is the inversive closure of L. We prove some properties of polynomials \(\chi _{K, F,\eta }(t)\) and use them for the study of the Krull-type dimension of the extension L/K. In the last part of the paper, we present a generalization of the obtained results to multidimensional filtrations of L/K associated with partitions of the sets of basic derivations and translations.

The feasibility of persistent fault analysis relies on special faults which can persist in all the rounds of block ciphers. This prerequisite can be positioned as a good fit into the FPGA scenario, which however has not been carefully exploited ever before. In this paper, we propose the persistent fault attack on the block cipher AES-128 implemented in FPGA where a new type of persistent fault is induced with the technique of Block RAM (BRAM) modification. The details of persistent fault injection are elaborated, especially on how the target bits of AES in BRAM can be identified and how they can be altered. Our experimental results show that: with the proposed attack, a simple statistical analysis can extract the secret key of AES-128 with S-Box implemented in BRAMs and protected by the countermeasure of inversive decryption based dual modular redundancy.

We show that an E-inversive semigroup S has a completely simple kernel KS if and only if it contains a primitive idempotent (in that case, KS is the set-theoretic union of the groups eSe, where e is a primitive idempotent of S). Along the way, some equivalent conditions for a semigroup to be E-inversive are given. Moreover, some applications of the above theorem will be pointed out.

This paper is inspired by Mitsch, Petrich, Reilly’s work on E – inversive semigroups and inverse semigroups. We first introduce the notions of a good subdirect product and a good surjective subhomo...

Optical orthogonal signature pattern codes (OOSPCs) play an important role in a novel type of optical code division multiple access (OCDMA) network for 2-dimensional image transmission. There is a one-to-one correspondence between an $$(m, n, w, \lambda )$$ -OOSPC and a $$(\lambda +1)$$ -(mn, w, 1) packing design admitting a point-regular automorphism group isomorphic to $${\mathbb {Z}}_m\times {\mathbb {Z}}_n$$ . In 2010, Sawa gave the first infinite class of (m, n, 4, 2)-OOSPCs by using S-cyclic Steiner quadruple systems. In this paper, we use various combinatorial designs such as strictly $${\mathbb {Z}}_m\times {\mathbb {Z}}_n$$ -invariant s-fan designs, strictly $${\mathbb {Z}}_m\times {\mathbb {Z}}_n$$ -invariant G-designs and rotational Steiner quadruple systems to present some constructions for (m, n, 4, 2)-OOSPCs. As a consequence, our new constructions yield more infinite families of optimal (m, n, 4, 2)-OOSPCs. Especially, we see that in some cases an optimal (m, n, 4, 2)-OOSPC can not achieve the Johnson bound. We also use Witt’s inversive planes to obtain optimal $$(p, p, p+1, 2)$$ -OOSPCs for all primes $$p\ge 3$$ .

This article analyzes the manifestation of the inversive relationship in the life cycle of the organization. Inversion is an internal contradiction in the hierarchy between the position of the hierarchical element, and its role. The reason for inversions is the discrepancy between the orientation of the organizational principles of hierarchy. The development of inversive relations leads the organization toward completion of its life cycle. Analysis of the inversive relationship in the hierarchy allows the comparative assessment of different models of the organizational life cycle.

We study high-dimensional numerical integration in the worst-case setting. The subject of tractability is concerned with the dependence of the worst-case integration error on the dimension. Roughly speaking, an integration problem is tractable if the worst-case error does not grow exponentially fast with the dimension. Many classical problems are known to be intractable. However, sometimes tractability can be shown. Often such proofs are based on randomly selected integration nodes. Of course, in applications, true random numbers are not available and hence one mimics them with pseudorandom number generators. This motivates us to propose the use of pseudorandom vectors as underlying integration nodes in order to achieve tractability. In particular, we consider digital inverse vectors and present two examples of problems, the weighted star discrepancy and integration of Hölder continuous, absolute convergent Fourier and cosine series, where the proposed method is successful.

In 2012, Diem introduced a new figure of merit for cryptographic sequences called expansion complexity. Recently, a series of paper has been published for analysis of expansion complexity and for testing sequences in terms of this new measure of randomness. In this paper, we continue this analysis. First we study the expansion complexity in terms of the Gr\"obner basis of the underlying polynomial ideal. Next, we prove bounds on the expansion complexity for random sequences. Finally, we study the expansion complexity of sequences defined by differential equations, including the inversive generator.

A semigroup S is called an E-inversive if for every aS there exists x in S Such that axE(s), where E(s) is the set of all idempotents of S, introduced by G.Thierrin. The concept of sub direct product of two E-inversive semigroups introduced by H. Mitsch by using the concept of sub homomorphism of inverse semigroups introduced by Mc Alisterand N.R.Reilly. The semidirect of two E-inversive semigroups introduced by F.Catino and M.M.Miccoli. In this paper we study some special identities in an E-inversive semigroup and we present preliminaries and basic concepts of E-inversive semigroups.

In this paper we study the distribution of very short sequences of inversive congruential pseudorandom numbers modulo $2^t$. We derive a new bound on exponential sums with such sequences and use it to give estimate their discrepancy. The technique we use, based the method of N. M. Korobov (1972) of estimating double Weyl sums and a fully explicit form of the Vinogradov mean value theorem due to K. Ford (2002), has never been used in this area and is very likely to find further applications.

Let $n$ be a positive integer. In this paper we provide a general theory to produce full orbit sequences in the affine $n$-dimensional space over a finite field. For $n=1$ our construction covers the case of the Inversive Congruential Generators (ICG). In addition, for $n>1$ we show that the sequences produced using our construction are easier to compute than ICG sequences. Furthermore, we prove that they have the same discrepancy bounds as the ones constructed using the ICG., To appear in Mathematics of Computation

In this paper we study semigroups defined either by means of weak inverses modulo Green’s relation \(\mathcal{{H}}\), or by means of the set of completely regular elements. Basic properties of E-inversive semigroups are analyzed, and semigroups whose completely regular elements form a subsemigroup or a rectangular band modulo \(\mathcal{{H}}\) are considered. We obtain results that generalize the corresponding results for E-semigroups or semigroups whose idempotents form a rectangular band, and also new results for E-inversive semigroups.

We introduce the new concept of joint nonlinear complexity for multisequences over finite fields and we analyze the joint nonlinear complexity of two families of explicit inversive multisequences. We also establish a probabilistic result on the behavior of the joint nonlinear complexity of random multisequences over a fixed finite field.

In this paper, we investigate strongly regular congruences on $E$-inversive semigroups $S$. We describe the complete lattice homomorphism of strongly regular congruences, which is a generalization of an open problem of Pastijn and Petrich for regular semigroups. An abstract characterization of left and right traces for strongly regular congruences is given. The strongly regular (sr) congruences on $E$-inversive semigroups $S$ are described by means of certain strongly regular congruence triples $({\it\gamma},K,{\it\delta})$ consisting of certain sr-normal equivalences ${\it\gamma}$ and ${\it\delta}$ on $E(S)$ and a certain sr-normal subset $K$ of $S$. Further, we prove that each strongly regular congruence on $E$-inversive semigroups $S$ is uniquely determined by its associated strongly regular congruence triple.

Given a circle $$C$$C of an inversive plane $${\mathcal {I}}$$I of order $$n$$n, the remaining circles are partitioned into three types according to the number of intersection points with $$C$$C. Let $${\mathcal {S}}$$S be the incidence structure formed by the points of $${\mathcal {I}}$$I and any two types of circles. It is proved that with some additional requirements, $${\mathcal {I}}$$I is the only inversive plane of order $$n$$n having $${\mathcal {S}}$$S as an induced substructure.

We consider Hilbert-type functions associated with finitely generated inversive difference field extensions and systems of algebraic difference equations in the case when the translations are assigned positive integer weights. We prove that such functions are quasi-polynomials that can be represented as alternating sums of Ehrhart quasi-polynomials of rational conic polytopes. In particular, we generalize the author’s results on difference dimension polynomials and their invariants to the case of inversive difference fields with weighted basic automorphisms.

In this paper we develop a relative Grobner basis method for a wide class of filtered modules. Our general setting covers the cases of modules over rings of differential, difference, inversive difference and difference–differential operators, Weyl algebras and multiparameter twisted Weyl algebras (the last class of rings includes the classes of quantized Weyl algebras and twisted generalized Weyl algebras). In particular, we obtain a Buchberger-type algorithm for constructing relative Grobner bases of filtered free modules.

In this paper we study the properties of homotopy inverses of comultiplications and algebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primarily interested in the algebraic loops which have inversive, power-associative and Moufang properties for some comultiplications.

We acknowledge priority of earlier and more general results than Theorem 1 of the paper referred to in the title.

A classical result due to Cohn states that a self-inversive polynomial has all its zeros on the unit circle if and only if all the zeros of its derivative lie in the closed unit disk. A more flexible necessary and sufficient condition than that of Cohn’s was given by Chen. However those results do not give any information on the simplicity of zeros of a self-inversive polynomial. This paper modifies the above results so that they serve as necessary and sufficient conditions for the simplicity as well as the unimodularity of zeros of a self-inversive polynomial.

In this article, we develop the Halton sequence of generating quasi-random numbers to an optimal sequence which has the inversive property. The new constructed quasi-random number generator satisfies the extra uniformity condition on [0, 1]. We finally present the performances of this generator in contrast to the former optimal Halton sequence in Chi et al. (2005) and modified optimal Halton sequence in Fathi et al. (2009).

We study connections between self-inversive and self-reciprocal polynomials, reduction theory of binary forms, minimal models of curves, and formally self-dual codes. We prove that if $\mathcal X$ is a superelliptic curve defined over $\mathbb C$ and its reduced automorphism group is nontrivial or not isomorphic to a cyclic group, then we can write its equation as $y^n = f(x)$ or $y^n = x f(x)$, where $f(x)$ is a self-inversive or self-reciprocal polynomial. Moreover, we state a conjecture on the coefficients of the zeta polynomial of extremal formally self-dual codes.

Let K be an inversive difference field, L a finitely generated inversive difference field extension of K, and F an intermediate inversive difference field of this extension. We prove the existence and establish properties and invariants of a numerical polynomial that describes the filtration of F induced by the natural filtration of the extension L/K associated with its generators. Then we introduce concepts of type and dimension of the extension L/K considering chains of its intermediate fields. Using properties of dimension polynomials of intermediate fields we obtain relationships between the type and dimension of L/K and difference birational invariants of this extension carried by its dimension polynomials. Finally, we present a generalization of the obtained results to the case of multivariate dimension polynomials associated with a given inversive difference field extension and a partition of the basic set of translations.

We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that such functions are quasi-polynomials, which can be represented as alternative sums of Ehrhart quasi-polynomials associated with rational conic polytopes. In particular, we obtain generalizations of main theorems on difference dimension polynomials and their invariants to the case of weighted basic difference operators., Comment: 16 pages

Referring mainly to the experiences of the patient, phenomenologicalanthropological diagnostics is shown as a supplement to a symptomatologicalcriteriological one. Since Greek Antiquity up to modern diagnostic glossaries there is the question of the structure of melancholia and mania and their interrelation. Recent issues of personality research, particularly under the aspect of “typus melancholicus” and “typus manicus” allow us to put these questions in a new way. We introduced two polar concepts, that of intolerance versus tolerance of ambiguity (of FrenkelBrunswik) and of “I” and “me” building up the self (G.H Mead). Deviant from obsessivecompulsive personality disorder we see the behavior of typus melancholicus mainly as hypernomic, compensating a primary lack of egoachievements. The preand intermorbid behavior of melancholics and of bipolars and manics, relate to each other in an inversive way of intolerance of ambiguity. Also the self in the melancholic episode, mainly oriented to the “me” (ObjectI) and that of mania to the “I” (SubjectI) shows the same inversive structure. This allows for a new understanding of the symptoms and phenomena in these states as the expression of a particular kind of depersonalisation in melancholia and of hyperpersonalisation in mania. Remarks on the psychotherapeutic guidance and rehabilitation are given.

(S, *) is a semigroup S equipped with a unary operation "*". This work is devoted to a class of unary semigroups, namely E- *-. A unary semigroup (S, *) is called an E-inversive *-semigroup if the following identities hold: , , . In this paper, E-inversive *-semigroups are characterized by several methods. Furthermore, congruences on these semigroups are also studied.

In the manner of Steiner’s interpretation of conics in the projective plane we consider a conic in a planar incidence geometry to be a pair consisting of a point and a collineation that does not fix that point. We say these loci are intrinsic to the collineation group because their construction does not depend on an imbedding into a larger space. Using an inversive model we classify the intrinsic conics in the hyperbolic plane in terms of invariants of the collineations that afford them and provide metric characterizations for each congruence class. By contrast, classifications that catalogue all projective conics intersecting a specified hyperbolic domain necessarily include curves which cannot be afforded by a hyperbolic collineation in the above sense. The metric properties we derive will distinguish the intrinsic classes in relation to these larger projective categories. Our classification emphasizes a natural duality among congruence classes induced by an involution based on complementary angles of parallelism relative to the focal axis of each conic, which we refer to as split inversion (Definition 5.3).

The paper describes an algebraic construction of the inversive differential ring, associated with a nonlinear control system, defined on a nonhomogeneous but regular time scale. The ring of meromorphic functions in system variables is constructed under the assumption that the system is submersive, and equipped with three operators (delta- and nabla-derivatives, and the forward shift operator) whose properties are studied. The formalism developed unifies the existing theories for continuous- and discrete-time nonlinear systems, and accommodates also the case of non-uniformly sampled systems. Compared with the homogeneous case the main difficulties are noncommutativity of delta (nabla) derivative and shift operators and the fact that the additional time variable t appears in the definition of the differential ring. The latter yields that the new variables of the inversive closure, depending on t, have to be chosen to be smooth at each dense point t of the time scale.

Consideration was given to the discrete-time queuing system with inversive servicing without interrupts, second-order geometrical arrivals, arbitrary (discrete) distribution of the customer length, and finite buffer. Each arriving customer has length and random volume. The total volume of the customers sojourning in the system is bounded by some value. Formulas of the stationary state probabilities and stationary distribution of the time of customer sojourn in the system were established.