On the extremal compatible linear connection of a generalized Berwald manifold

Generalized Berwald manifolds are Finsler manifolds admitting linear connections such that the parallel transports preserve the Finslerian length of tangent vectors (compatibility condition). It is known (Vincze in J AMAPN 21:199–204, 2005) that such a linear connection must be metrical with respect to the averaged Riemannian metric given by integration of the Riemann-Finsler metric on the indicatrix hypersurfaces. Therefore the linear connection (preserving the Finslerian length of tangent vectors) is uniquely determined by its torsion. If the torsion is zero then we have a classical Berwald manifold. Otherwise, the torsion is some strange data we need to express in terms of the intrinsic quantities of the Finsler manifold. The paper presents the idea of the extremal compatible linear connection of a generalized Berwald manifold by minimizing the pointwise length of its torsion tensor. It is uniquely determined because the number of the Lagrange multipliers is equal to the number of the equations for the compatibility of the linear connection with the Finslerian metric. Using the reference element method, the extremal compatible linear connection can be expressed in terms of the canonical data as well. It is an intrinsic algorithm to check the existence of compatible linear connections on a Finsler manifold because it is equivalent to the existence of the extremal compatible linear connection.

MEAN–VARIANCE INSURANCE DESIGN WITH COUNTERPARTY RISK AND INCENTIVE COMPATIBILITY

This paper studies the optimal insurance design from the perspective of an insured when there is possibility for the insurer to default on its promised indemnity. Default of the insurer leads to limited liability, and the promised indemnity is only partially recovered in case of a default. To alleviate the potential ex post moral hazard, an incentive compatibility condition is added to restrict the permissible indemnity function. Assuming that the premium is determined as a function of the expected coverage and under the mean–variance preference of the insured, we derive the explicit structure of the optimal indemnity function through the marginal indemnity function formulation of the problem. It is shown that the optimal indemnity function depends on the first and second order expectations of the random recovery rate conditioned on the realized insurable loss. The methodology and results in this article complement the literature regarding the optimal insurance subject to the default risk and provide new insights on problems of similar types.

Normalized solutions to a Schrödinger–Bopp–Podolsky system under Neumann boundary conditions

In this paper, we study a Schrödinger–Bopp–Podolsky (SBP) system of partial differential equations in a bounded and smooth domain of [Formula: see text] with a nonconstant coupling factor. Under a compatibility condition on the boundary data we deduce existence of solutions by means of the Ljusternik–Schnirelmann theory.

Sharp conditions for the linearization of finite elasticity

We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can be strictly lower than the minimal value of the standard linear elastic energy if a strict compatibility condition for external loads does not hold. The results are provided for both the compressible and the incompressible case.

-ALGEBRAS ASSOCIATED WITH TWO-SIDED SUBSHIFTS

This paper is a continuation of the paper, Matsumoto [‘Subshifts, $\lambda $ -graph bisystems and $C^*$ -algebras’, J. Math. Anal. Appl. 485 (2020), 123843]. A $\lambda $ -graph bisystem consists of a pair of two labeled Bratteli diagrams satisfying a certain compatibility condition on their edge labeling. For any two-sided subshift $\Lambda $ , there exists a $\lambda $ -graph bisystem satisfying a special property called the follower–predecessor compatibility condition. We construct an AF-algebra ${\mathcal {F}}_{\mathcal {L}}$ with shift automorphism $\rho _{\mathcal {L}}$ from a $\lambda $ -graph bisystem $({\mathcal {L}}^-,{\mathcal {L}}^+)$ , and define a $C^*$ -algebra ${\mathcal R}_{\mathcal {L}}$ by the crossed product . It is a two-sided subshift analogue of asymptotic Ruelle algebras constructed from Smale spaces. If $\lambda $ -graph bisystems come from two-sided subshifts, these $C^*$ -algebras are proved to be invariant under topological conjugacy of the underlying subshifts. We present a simplicity condition of the $C^*$ -algebra ${\mathcal R}_{\mathcal {L}}$ and the K-theory formulas of the $C^*$ -algebras ${\mathcal {F}}_{\mathcal {L}}$ and ${\mathcal R}_{\mathcal {L}}$ . The K-group for the AF-algebra ${\mathcal {F}}_{\mathcal {L}}$ is regarded as a two-sided extension of the dimension group of subshifts.

Of one over determined system differential equations at private derivative second order with one singular lines in general case

In this paper, an over determined system of second-order partial differential equations with a single singular line in the General case is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with a single singular line in the General case. If the compatibility condition is met, integral representations of the variety of solutions are found explicitly in terms of three arbitrary constants, when the singular line is in the boundaries of the domain for which initial data problems (Cauchy-type Problems) can be set.

Integral representation of solution manifolds for over determined systems with one singular line

In this paper, an over determined system of second-order partial differential equations with one singular line is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with one singular line. Under the condition of compatibility, introducing a new function, we come to a over determined system of partial differential equations of the second order with one singular line of a simpler form. The integral representation of the manifold of solutions of the redefined second-order partial differential system with one singular line is found explicitly through three arbitrary constants, for which initial data problems (Cauchy type problems) can be posed.

Of one over determined system differential equation at private derivative second order with one singular point and one singular line

In this paper, a over determined system of second-order partial differential equations with one singular point and one singular line is investigated. A compatibility condition is found for over determined systems of second-order partial differential equations with one singular point and one singular line. If the compatibility condition is met, integral representations of the variety of solutions are found explicitly in terms of three arbitrary constants, when the singular line is in the boundaries of the domain for which initial data problems (Cauchy-type Problems) can be set. In this paper considers a redefined system of second-order partial differential equations, when the coefficients and right parts have one singular point and one singular line. Obtaining a variety of solutions and studying boundary value problems for linear differential equations of the hyperbolic type of the second order, some linear redefined systems of the first and second order with one and two supersingular lines and supersingular points is devoted to the monograph of academician of the National Academy of Sciences of the Republic of Tatarstan Rajabov N. - 1992 "Introduction to the theory of partial differential equations with supersingular coefficients" [6, p.126]. Using the obtained results of The monograph of Rajabov N., a variety of solutions of redefined systems of partial differential equations of the second order with one singular point and one singular line in an explicit form, through three arbitrary constants, was found.

Phase-inherent linear visco-elasticity model for infinitesimal deformations in the multiphase-field context

A linear visco-elasticity ansatz for the multiphase-field method is introduced in the form of a Maxwell-Wiechert model. The implementation follows the idea of solving the mechanical jump conditions in the diffuse interface regions, hence the continuous traction condition and Hadamard’s compatibility condition, respectively. This makes strains and stresses available in their phase-inherent form (e.g. $$\varepsilon ^{\alpha }_{ij}$$ ε ij α , $$\varepsilon ^{\beta }_{ij}$$ ε ij β ), which conveniently allows to model material behaviour for each phase separately on the basis of these quantities. In the case of the Maxwell-Wiechert model this means the introduction of phase-inherent viscous strains. After giving details about the implementation, the results of the model presented are compared to a conventional Voigt/Taylor approach for the linear visco-elasticity model and both are evaluated against analytical and sharp-interface solutions in different simulation setups.