Baryogenesis and neutron-antineutron oscillation at TeV

We propose a TeV extension of the standard model to generate the cosmological baryon asymmetry with an observable neutron-antineutron oscillation. The new fields include a singlet fermion, an isotriplet and two isosinglet diquark scalars. There will be no proton decay although the Majorana mass of the singlet fermion as well as the trilinear couplings between one isosinglet diquark and two isotriplet diquarks softly break the baryon number of two units. The isosinglet diquarks couple to two right-handed down-type quarks or to a right-handed up-type quark and a singlet fermion, whereas the isotriplet diquark couples to two left-handed quarks. The isosinglet diquarks mediate the three-body decays of the singlet fermion to realize a TeV baryogenesis without fine tuning the resonant effect. By the exchange of one singlet fermion and two isosinglet diquarks and of one isosinglet diquark and two isotriplet diquarks, a neutron-antineutron oscillation is allowed to verify in the future experiments.     

Chaotic dynamics of the heat semigroup on Riemannian symmetric spaces

We show that the heat semigroup generated by certain perturbations of the Laplace–Beltrami operator on the Riemannian symmetric spaces of noncompact type is chaotic   on their L^p$L^p$-spaces when 2<p<∞$2<p<\infty$. Both the range of p and the range of chaos-inducing perturbation are sharp. This extends a result of Ji and Weber [17] where it was shown that under identical conditions the heat operator is subspace-chaotic on these spaces.     

Macdonald polynomials as characters of Cherednik algebra modules

We prove that Macdonald polynomials are characters of irreducible Cherednik algebra modules.     

Wandering Subspaces of the Bergman Space and the Dirichlet Space Over {{\mathbb{D}^{n}}}

Doubly commuting invariant subspaces of the Bergman space and the Dirichlet space over the unit polydisc \({\mathbb{D}^n}\) (with \({n \geq 2}\) ) are investigated. We show that for any non-empty subset \({\alpha=\{\alpha_1,\ldots,\alpha_k\}}\) of \({\{1,\ldots,n\}}\) and doubly commuting invariant subspace \({\mathcal{S}}\) of the Bergman space or the Dirichlet space over \({\mathbb{D}^n}\) , restriction of the multiplication operator tuple on \({\mathcal{S}, M_{\alpha}|_\mathcal{S}:=(M_{z_{\alpha_1}}|_\mathcal{S},\ldots, M_{z_{\alpha_k}}|_\mathcal{S})}\) , always possesses generating wandering subspace of the form $$\bigcap_{i=1}^k(\mathcal{S}\ominus z_{\alpha_i}\mathcal{S})$$ .     

Endomorphism Algebras of Some Modules for Schur Algebras and Representation Dimension

We consider the representation dimension, for fixed n ≥ 2, of ordinary and quantised Schur algebras S(n, r) over a field k. For k of positive characteristic p we give a lower bound valid for all p. We also give an upper bound in the quantum case, when k has characteristic 0.     

Maximal Contractive Tuples

Maximality of a contractive tuple of operators is considered. A characterization for a contractive tuple to be maximal is obtained. The notion of maximality for a submodule of the Drury–Arveson module on the \(d\) -dimensional unit ball \({\mathbb {B}}_d\) is defined. For \(d=1\) , it is shown that every submodule of the Hardy module over the unit disc is maximal. But for \(d\ge 2\) we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of maximal submodules is obtained.     

Exact multiplicity for the perturbed Q-curvature problem in {\mathbb{R}^N,N \geq 5}

Let N ≥ 5 and \({{\mathcal{D}}^{2,2} (\mathbb{R}^N)}\) denote the closure of \({C_0^\infty (\mathbb{R}^N)}\) in the norm \({\|u\|_{{\mathcal{D}}^{2,2} (\mathbb{R}^N)}^2 := \int\nolimits_{\mathbb{R}^N} |\Delta u|^2.}\) Let \({K \in C^2 (\mathbb{R}^N).}\) We consider the following problem for ? ≥ 0: $$(P_\varepsilon) \left\{\begin{array}{llll}{\rm Find} \, u \in {\mathcal{D}}^{2, 2} (\mathbb{R}^N) \, \, {\rm solving} :\\ \left.\begin{array}{lll}\Delta^2 u = (1+ \varepsilon K (x)) u^{\frac{N+4}{N-4}}\\ u > 0 \end{array}\right\}{\rm in} \, \mathbb{R}^N.\end{array}\right.$$ We show an exact multiplicity result for (P _? ) for all small ? > 0.     

Small secret exponent attack on RSA variant with modulus N=p^rq

We consider an RSA variant with Modulus \(N=p^rq\) . This variant is known as Prime Power RSA. In PKC 2004, May proved when decryption exponent \(d<N^{ \frac{r}{(r+1)^2}}\) or \(d< N^{\left( \frac{r-1}{r+1}\right) ^2}\) , one can factor \(N\) in polynomial time. In this paper, we improve this bound when \(r \le 5\) . We provide detailed experimental results to justify our claim.     

A Skew-Duoidal Eckmann-Hilton Argument and Quantum Categories

A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory whose morphisms are spans between sets. Quantum categories were originally defined as monoidal comonads on endomorphism objects in a particular monoidal bicategory ?. Then they were shown also to be skew monoidal structures (with an appropriate unit) on objects in ?. Now we see in what kind of ? quantum categories are merely monads.     

Biomimetic growth of gallic acid–ZnO hybrid assemblies and their applications

In this study, we probed the biomimetic formation of gallic acid (GA)–ZnO nanoparticle hybrids. It was found that the morphologies formed were dependent upon pH values, resulting in GA–ZnO hybrids of varying shapes such as micro or nanoplates or fibers. The formed supramolecular GA–ZnO hybrids were found to be luminescent as indicated by confocal microscopy and were utilized for the photocatalytic degradation of the organic dye methylene blue. We also explored the bactericidal effects of the hybrids on Staphylococcus aureus (S. aureus) as well as Escherichia Coli (E. Coli). Thus, we have developed a new class of shape-controlled nanohybrid assemblies via mild, green synthetic methods that may be utilized for photocatalytic degradation for environmental remediation as well as for antibacterial applications.