On weights in duadic abelian codes

In this note, we prove that if C is a duadic binary abelian code with splitting μ=μ₋₁ and the minimum odd weight of C satisfies d²−d+1≠n, then d(d−1)n+11. We show by an example that this bound is sharp. A series of open problems on this subject are proposed.     

An adaptive parameter approach for an approximate solution of optimal control problems

In this paper, we consider a class of nonlinear optimal control problems (Bolza-problems) with constraints of the control vector, initial and boundary conditions of the state vectors. The time interval is fixed. Our approach to parametrize both the state functions and the control functions is described by general piecewise polynomials with unknown coefficients (parameters), where a fixed partition of the time interval is used. Here each of these functions in a suitable way individually will be approximated by such polynomials. The optimal control problem thus is reduced to a mathematical programming problem for these parameters. The existence of an optimal solution is assumed. Convergence properties of this method are not considered in this paper.     

Generalized vector valued almost periodic and ergodic distributions

Schwartz's almost periodic distributions are generalized to the case of Banach space valued distributions , and furthermore for a given arbitrary class A to for φ∈ test functions D(R,C)}. It is shown that this extension process is iteration complete, i.e. . Moreover the T from are characterized in various ways, also tempered distributions with P={X-valued functions of polynomial growth} are shown. Under suitable assumptions , , where for all h>0}, is defined with the corresponding extension of Mh. With an extension of the indefinite integral from to D^′(R,X) a distribution analogue to the Bohl-Bohr-Amerio-Kadets theorem on the almost periodicity of bounded indefinite integrals of almost periodic functions is obtained, also for almost automorphic, Levitan almost periodic and recurrent functions, similar for a result of Levitan concerning ergodic indefinite integrals. For many of the above results a new (Δ)-condition is needed, we show that it holds for most of the A needed in applications. Also an application to the study of asymptotic behavior of distribution solutions of neutral integro-differential-difference systems is given.     

第三类模糊事件的模糊概率

研究第三类模糊概率--模糊事件模糊概率的数学描述.在区间概率和第二类模糊概率的基础上,进一步给出了第三类离散型模糊概率的随机变量及其模糊分布函数和模糊分布列的定义和性质以及数字特征,并研究了连续型模糊概率随机变量的模糊数学期望和模糊方差的定义,进一步完善了模糊概率理论.