In this paper, we consider the maximizing of probability $${\mathbb {P}}\left\{ \, \zeta \mid \in {\mathbf {K}}({\mathbf {x}}) \right\} $$ over a closed and convex set $${\mathcal {X}}$$ , special case chance-constrained optimization problem. Suppose $${\mathbf \triangleq \left\{ {\mathcal {K}}\, c({\mathbf {x}},\zeta ) \ge 0 $$\zeta is uniformly distributed on compact {K}}$$ $$c({\mathbf )$$ d...

For a Hopf algebra H over a commutative ring k, the category MH of right Hopf modules is equivalent to the category Mk of k-modules, that is, the comparison functor −⊗k H : Mk → MH is an equivalence (Fundamental theorem of Hopf modules). This was proved by Larson and Sweedler via the notion of coinvariants McoH for any M ∈ MH . The coinvariants functor (−) coH : MH → Mk is right adjoint to the ...

A pharmacological screen identified the H+ and K+ ATPase transporter as obligatory for normal orientation of the left-right body axis in Xenopus. Maternal H+/K+-ATPase mRNA is symmetrically expressed in the 1-cell Xenopus embryo but becomes localized during the first two cell divisions, demonstrating that asymmetry is generated within two hours postfertilization. Although H+/K+-ATPase subunit m...

After we have ne-tuned the right-handed CKM matrix to satisfy the bounds for CP violation K in K meson systems, the right-handed charged current gauge boson W R is shown to substantially aaect CP asymmetries in B systems. The joint 2 analysis is applied to CKM experiments and to B ? B mixing to constrain the standard CKM and the right-handed CKM matrix elements. In (sin (2); sin (2)), (x s ; si...

After we have fine-tuned the right-handed CKM matrix to satisfy the bounds for CP violation K in K meson systems, the right-handed charged current gauge boson WR is shown to substantially affect CP asymmetries in B systems. The joint χ2 analysis is applied to CKM experiments and to B − B̄ mixing to constrain the standard CKM and the right-handed CKM matrix elements. In (sin (2α), sin (2β)), (xs,...

Difference sets have been extensively studied in groups, principally in Abelian groups. Here we extend the notion of a difference set to loops. This entails considering the class of principal block partial designs (PBPDs) and (v, k, A) designs. By means of a certain permutation matrix decomposition of the incidence matrices of a system and...

Abstract The matrix $A:{{\mathbb{R}}}^n \to{{\mathbb{R}}}^m$ is $(\delta ,k)$-regular if for any $k$-sparse vector $x$, $$\begin{align*} & \left| \|Ax\|_2^2-\|x\|_2^2\right| \leq \delta \sqrt{k} \|x\|_2^2. \end{align*}$$We show that $A$ $1 k 1/\delta ^2$, then by multiplying the columns of independent random signs, resulting ensemble $A_\varepsilon $ acts on an arbitrary subset $T \subset{{...

Simon's problem plays an important role in the history of quantum algorithms, as it inspired Shor to discover celebrated algorithm solving integer factorization polynomial time. Besides, for has been recently applied break symmetric cryptosystems. Generalized problem, denoted by $\mathsf{GSP}(p,n,k)$, is a natural extension problem. In this paper we consider query complexity $\mathsf{GSP}(p,n,k...

Data mining is a powerful tool for firms to extract knowledge from their customers’ transaction data. One of the useful applications of data mining is segmentation. Segmentation is an effective tool for managers to make right marketing strategies for right customer segments. In this study we have segmented retailers of a hygienic manufacture. Nowadays all manufactures do understand that for st...

If k is a field and R commutative k-algebra, we explore the question of when ring DR|k k-linear differential operators on isomorphic to its opposite ring. Under mild hypotheses, prove this case whenever Gorenstein local or invariants. As key step in proof show that many cases interest canonical modules admit right D-module structures.