For fixed complex q with |q| > 1, the q-logarithm Lq is the meromorphic continuation of the series ∑ n>0 z / q −1 , |z| < |q|, into the whole complex plane. IfK is an algebraic number field, one may ask if 1, Lq 1 , Lq c are linearly independent over K for q, c ∈ K× satisfying |q| > 1, c / q, q2, q3, . . .. In 2004, Tachiya showed that this is true in the Subcase K Q, q ∈ Z, c −1, and the prese...

This paper follows the recent discussion on the sparse solution recovery with quasi-norms lq, q ∈ (0, 1) when the sensing matrix possesses a Restricted Isometry Constant δ2k (RIC). Our key tool is an improvement on a version of “the converse of a generalized Cauchy-Schwarz inequality” extended to the setting of quasi-norm. We show that, if δ2k ≤ 1/2, any minimizer of the lq minimization, at lea...

A stochastic linear quadratic (LQ) control problem is indefinite when the cost weighting matrices for the state and the control are allowed to be indefinite. Indefinite stochastic LQ theory has been extensively developed and has found interesting applications in finance. However, there remains an outstanding open problem, which is to identify an appropriate Riccati-type equation whose solvabili...

Four mature rumen and abomasal cannulated wethers were used in a 2 x 2 reversal experiment to study the effect of forage quality on daily quantity of abomasal protein and microbial protein synthesis. Diets were either high quality [HOo 16.4% crude protein (CP)] or low quality (LOo 9.3% CP) Coastal bermudagrass which provided 110.7 and 58.3 g CP intake daily, respectively. Non-ammonia CP reachin...

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We study the relation between Sobolev inequalities for differential forms on a Riemannian manifold (M, g) and the Lq,p-cohomology of that manifold. The Lq,p-cohomology of (M,g) is defined to be the quotient of the space of closed differential forms in L(M) modulo the exact forms which are exterior differentials of forms in L(M).

The length function lq(r,R) is the smallest length of a q-ary linear code of covering radius R and codimension r. New upper bounds on lq(r, 2) are obtained for odd r ≥ 3. In particular, using the one-to-one correspondence between linear codes of covering radius 2 and saturating sets in the projective planes over finite fields, we prove that

This paper presents LQ control problem based on numerical computation with guaranteed accuracy. By using the proposed methods, it is possible to guarantee numerical quality about design of control system. This paper also proposes a problem which finds the numerical optimal controller from a set of solutions solved by verified LQ control problem.