Division with remainder in algebras with valuation

To any integral algebra with valuation an abelian group is associated, which measures how much the uniqueness of the division with remainder is violated. The analogy with the divisor class group is discussed. Examples of such groups are computed in cases of formal local rings of some cusps on an algebraic curve.     

Division with remainder in algebras with valuation

To any integral algebra with valuation an abelian group is associated, which measures how much the uniqueness of the division with remainder is violated. The analogy with the divisor class group is discussed. Examples of such groups are computed in cases of formal local rings of some cusps on an algebraic curve.     

Brownian motion with drift on spaces with varying dimension

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel’s principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift.     

Fuzzy带算子环和Fuzzy带算理想

提出Fuzzy带算子环、Fuzzy带算理想和Fuzzy带算商环的定义,讨论它们的一些初等性质。     

桥本甲状腺炎合并甲状腺癌的危险因素回归分析

目的 探讨桥本甲状腺炎（HT）合并甲状腺癌的危险因素。方法 采用回顾性病例对照研究,选取59 例HT 合并甲状腺癌患者为病例组,按照1∶2比例选取118 例HT 合并甲状腺良性结节或单纯HT 患者为对照组,对相关因素进行单因素和多因素logistic 回归分析。结果 单因素分析显示甲状腺疾病家族史、碘摄入情况、辐射接触史、甲状腺自身抗体和合并单发结节为HT 合并甲状腺癌的影响因素。经多因素分析家族史、高碘摄入、辐射接触史为HT 合并甲状腺癌的危险因素,其OR 值（95%CI）分别为2.141（1.664~2.755）、2.479（1.895~2.936）和4.596（3.693~4.997）。结论 HT 合并甲状腺癌发病机制有待于进一步研究,应针对危险因素(家族史、碘摄入情况、辐射接触史)采取措施进行早防早治。     

Records with confirmation

In the present paper, the concept of records with confirmation is proposed. This new concept implies that such records cannot be contaminated with sample outliers. On determining records with confirmation, we discuss their distributional and limit properties. A test based on records with confirmation is provided in our work. We also present simulation techniques for generating record values with confirmation.     

Categories with families and first-order logic with dependent sorts

First-order logic with dependent sorts, such as Makkai's first-order logic with dependent sorts (FOLDS), or Aczel's and Belo's dependently typed (intuitionistic) first-order logic (DFOL), may be regarded as logic enriched dependent type theories. Categories with families (cwfs) is an established semantical structure for dependent type theories, such as Martin-Löf type theory. We introduce in this article a notion of hyperdoctrine over a cwf, and show how FOLDS and DFOL fit in this semantical framework. A soundness and completeness theorem is proved for DFOL. The semantics is functorial in the sense of Lawvere, and uses a dependent version of the Lindenbaum-Tarski algebra for a DFOL theory. Agreement with standard first-order semantics is established. Applications of DFOL to constructive mathematics and categorical foundations are given. A key feature is a local propositions-as-types principle.     

Semi-orthogonal spline-wavelets with derivatives and the algorithm with splitting

This paper deals with the use of a scalar product with derivatives for constructing semi-orthogonal spline-wavelets. The reduction of supports of such wavelets in comparison with the classical semi-orthogonal wavelets is shown. For splines of the third degree, the algorithm of wavelet-transformation in the formof the solution to a three-diagonal systemof linear equations with strict diagonal prevalence has been obtained. The results of numerical experiments on the calculation of derivatives of a discretely given function are presented.     

Differential equations with conical degeneration in spaces with asymptotics

We define a space with asymptotics isomorphic to the direct sum of the corresponding Sobolev spaces for any values of their indices. In spaces with asymptotics, we consider problems for differential operators with conical degeneration and state conditions providing their Fredholm property.     

Operators with Singular Trace Conditions on a Manifold with Edges

We establish a new calculus of pseudodifferential operators on a manifold with smooth edges and study ellipticity with extra trace and potential conditions (as well as Green operators) at the edge. In contrast to the known scenario with conditions of that kind in integral form we admit in this paper ‘singular’ trace and Green operators. In contrast to standard conditions in the theory of elliptic boundary value problems (like Dirichlet or Neumann conditions) our singular trace conditions, in general, do not act on functions that are smooth up to the boundary, but admit a more general asymptotic structure. Their action is now associated with the Laurent coefficients of the meromorphic Mellin transforms of functions with respect to the half-axis variable, the distance to the edge.     

Equations with Random Gaussian Operators with Unbounded Mean Value

We consider an equation in a Hilbert space with a random operator represented as a sum of a deterministic, closed, densely defined operator and a Gaussian strong random operator. We represent a solution of an equation with random right-hand side in terms of stochastic derivatives of solutions of an equation with deterministic right-hand side. We consider applications of this representation to the anticipating Cauchy problem for a stochastic partial differential equation.     

Queueing systems with inventory management with random lead times and with backordering

We investigate M/M/1/∞-systems with inventory management, continuous review, exponentially distributed lead times and backordering. We compute performance measures and derive optimality conditions under different order policies. For performance measures, which are not explicitly at hand, we present an approximation scheme for all possible parameter combinations. Although we cannot completely determine analytically the steady state probabilities for the system we are able to derive functional relations between interesting probabilities and show surprising insensitivity properties of several performance measures. For the approximations we develop an algorithm adapted to the system structure which suggests easy adaption to other systems.Work supported by Deutscher Akademischer Austauschdienst and KBN, Poland, Project D/02/32206.     

Manifolds with Cusps

In this paper manifolds with cusps are defined and their properties investigated. Manifolds with cusps are manifolds with boundary where the dimension of the tangent cone at points varies widely with that point. Examples are exponential sums, splines, and polynomials with only real roots. The investigations are motivated by numerical algorithms in approximation theory and other areas.     

Prime Rings with Involution Equipped with Some New Product

Let R be a ring with involution *. We consider R as a ring equipped with a new product r s = rs + sr^*. The relationship between (ordinary) ideals of R and right ideals of R with respect to the product is studied.AMS Subject Classification (2000): 16W10, 16D25     

Insider Models with Finite Utility in Markets with Jumps

In this article we consider, under a Lévy process model for the stock price, the utility optimization problem for an insider agent whose additional information is the final price of the stock blurred with an additional independent noise which vanishes as the final time approaches. Our main interest is establishing conditions under which the utility of the insider is finite. Mathematically, the problem entails the study of a “progressive” enlargement of filtration with respect to random measures. We study the jump structure of the process which leads to the conclusion that in most cases the utility of the insider is finite and his optimal portfolio is bounded. This can be explained financially by the high risks involved in models with jumps.     

SDEs with constraints driven by semimartingales and processes with bounded p-variation

We study the existence, uniqueness and stability of solutions of general stochastic differential equations with constraints driven by semimartingales and processes with bounded $p$-variation. Applications to SDEs with constraints driven by fractional Brownian motion and standard Brownian motion are given.     

Einstein-maxwell equations compatible with certain killing vectors with light velocity

Summary In this paper, we study the basic system consisting of the Einstein's field equations and the Maxwell equations for the non-null electromagnetic field. A new differential geometric approach has been presented to obtain the necessary and sufficient conditions for the compatibility of the field equations with certain Killing vectors with light velocity. Finally, with respect to this new approach, we examine some geometric changes in the compatibility condition of the basic system with the continuity equation. Entrata in Redazione il 22 novembre 1977. This research was supported by the National Research Council of Canada.     

Tuberculosis model with relapse via fractional conformable derivative with power law

The present study explores the tuberculosis dynamics with relapse with a nonlocal conformable derivative in the Caputo sense. The real data of tuberculosis cases since 2002 to 2017 are used to the set the parameters. The numerical results with the realistic parameters are chosen and present the graphical results. Further, we assign different values to the fractional parameters α and β and discuss its effect on the system variables. The use of these two fractional operators on the model simultaneously with realistic data gives reliable results.     

Algebras with bracket

An algebra with bracket is an associative algebra A equipped with a bilinear operation [−,−] satisfying [a · b, c] = [a, c]·b+a · [b, c]. Our main result claims that the operad corresponding to algebras with bracket is Koszul.     

因式分解范畴

本文研究因式分解范畴，得到与因式分解范畴等价的范畴仍为因式分解范畴．