Let $R$ be a commutative Noetherian ring and ${\mathfrak a}$ an ideal of $R$. We introduce the concept of ${\mathfrak a}$-weakly Laskerian $R$-modules, and we show that if $M$ is an ${\mathfrak a}$-weakly Laskerian $R$-module and $s$ is a non-negative integer such that ${\rm Ext}^j_R(R/{\mathfrak a}, H^i_{{\mathfrak a}}(M))$ is ${\mathfrak a}$-weakly Laskerian for all $i<s$ and all $j$, then for any ${\mathfrak a}$-weakly Laskerian submodule $X$ of $H^s_{{\mathfrak a}}(M)$, the $R$-module ${\rm Hom}_R(R/{\mathfrak a},H^s_{{\mathfrak a}}(M)/X)$ is ${\mathfrak a}$-weakly Laskerian. In particular, the set of associated primes of $H^s_{\mathfrak a}(M)/X$ is finite. As a consequence, it follows that if $M$ is a finitely generated $R$-module and $N$ is an ${\mathfrak a}$-weakly Laskerian $R$-module such that $ H^i_{{\mathfrak a}}(N)$ is ${\mathfrak a}$-weakly Laskerian for all $i<s$, then the set of associated primes of $H^s_{\mathfrak a}(M, N)$ is finite. This generalizes the main result of S. Sohrabi Laleh, M. Y. Sadeghi, and M. Hanifi Mostaghim (2012).
Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.
In this paper, a generalized bivariate lifetime distribution is introduced. This new model is constructed based on a dependent model consisting of two parallel-series systems which have a random number of parallel subsystems with fixed components connected in series. The probability that one system fails before the other one is measured by using competing risks. Using the extreme-value copulas, the dependence structure of the proposed model is studied. Kendall's tau, Spearman's rho and tail dependences are investigated for some special cases. Simulation results are given to examine the effectiveness of the proposed model.
We prove a generalized maximum principle for subsolutions of boundary value problems, with mixed type unilateral conditions, associated to a degenerate parabolic second-order operator in divergence form.
In the current work, a new notion of n-weak amenability of Banach algebras using homomorphisms, namely (ϕ, ψ)-n-weak amenability is introduced. Among many other things, some relations between (ϕ, ψ)-n-weak amenability of a Banach algebra A and Mm(A), the Banach algebra of m × m matrices with entries from A, are studied. Also, the relation of this new concept of amenability of a Banach algebra and its unitization is investigated. As an example, it is shown that the group algebra L 1 (G) is (ϕ, ψ)-n-weakly amenable for any bounded homomorphisms ϕ and ψ on L 1 (G).
In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined for decoupling these outputs and for their perfect trajectory tracking. The control of robotic manipulation is investigated. These are mechanical structures more complex than conventional serial-linkage arms. The robotic hand with possible inner contacts is a paradigm of general manipulation systems. Unilateral contacts between mechanical parts make the control of manipulation system quite involved. In fact, contacts can be considered as unactuated (passive) joints. The main goal of dexterous manipulation consists of controlling the motion of the manipulated object along with the grasping forces exerted on the object. In the robotics literature, the general problem of force/motion control is known as "hybrid control". This paper is focused on the decoupling and functional controllability of contact forces and object motions. The goal is to synthesize a control law such that each output vector, namely the grasping force and the object motion, can be independently controlled by a corresponding set of generalized input forces. The functional force/motion controllability is investigated. It consists of achieving force and motion tracking with no error on variables transients. The framework used in this paper is the geometric approach to the structural synthesis of multivariable systems.
We deal with a suitable weak solution (v, p) to the Navier-Stokes equations in a domain Ω ⊂ R 3 . We refine the criterion for the local regularity of this solution at the point (fx0, t0), which uses the L 3 -norm of v and the L 3/2 -norm of p in a shrinking backward parabolic neighbourhood of (x0, t0). The refinement consists in the fact that only the values of v, respectively p, in the exterior of a space-time paraboloid with vertex at (x0, t0), respectively in a ''small'' subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point (x0, t0) if v and p are “smooth” outside the paraboloid.
Nevus lipomatosus superficialis is a rare hamartomatous malformation which is composed of ectopic adipocytes in the dermis. It was first reported in 1921 by Hoffmann and Zurhelle. Two clinical forms of nevus lipomatosus superficialis have been described: classical (multiple) and solitary. Classical form of nevus lipomatosus superficialis is usually found on pelvic girdle, trunk, buttocks and thighs as soft, skin colored papules or nodules. It is usually present at birth or it appears in the first two decades of life. The solitary form of lipomatosus superficialis appears as a solitary papule or nodule on the back, scalp and arms of the patients with late onset. The lesions are usually asymptomatic, however some patients may complain about pain and itching. Malignant transformation of nevus lipomatosis superficialis has not been reported yet. Therefore, surgical intervention is only necessary for the patients who have cosmetic concerns. Recurrence after surgical removal is very rare. Perineum is an uncommon localization for nevus lipomatosus superficialis. Hereby, we report a 55-year-old Caucasian female with a 6x5,5x4 cm mass in the perineal region. The patient had cosmetic concerns, therefore she wanted the lesion to be removed surgically. The lesion was surgically removed. The histopathological evaluation of the specimen revealed nevus lipomatosus superficialis. A solitary type of giant nevus lipomatosus superficialis in the perineal region of a patient over the age of 50 is a very rare condition. Even rarely seen, nevus lipomatosus superficialis should be kept in mind in the differential diagnosis of perineal masses., Funda Tamer, Mehmet Eren Yuksel, and Literatura
Let $\Omega$ be a bounded open subset of $\mathbb{R}^{n}$, $n>2$. In $\Omega$ we deduce the global differentiability result \[u \in H^{2}(\Omega, \mathbb{R}^{N}) \] for the solutions $u \in H^{1}(\Omega, \mathbb{R}^{n})$ of the Dirichlet problem \[ u-g \in H^{1}_{0}(\Omega, \mathbb{R}^{N}), -\sum _{i}D_{i}a^{i}(x,u,Du)=B_{0}(x,u,Du) \] with controlled growth and nonlinearity $q=2$. The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.
This paper introduces a neurodynamics optimization model to compute the solution of mathematical programming with equilibrium constraints (MPEC). A smoothing method based on NPC-function is used to obtain a relaxed optimization problem. The optimal solution of the global optimization problem is estimated using a new neurodynamic system, which, in finite time, is convergent with its equilibrium point. Compared to existing models, the proposed model has a simple structure, with low complexity. The new dynamical system is investigated theoretically, and it is proved that the steady state of the proposed neural network is asymptotic stable and global convergence to the optimal solution of MPEC. Numerical simulations of several examples of MPEC are presented, all of which confirm the agreement between the theoretical and numerical aspects of the problem and show the effectiveness of the proposed model. Moreover, an application to resource allocation problem shows that the new method is a simple, but efficient, and practical algorithm for the solution of real-world MPEC problems.