We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our has two loops. The inner loop computes the risk by solving saddle-point problem. outer performs $Q-$ learning compute an optimal policy. Several widely investigated measures (e.g., conditional value-at-risk, optimized certainty equivalent, and absolute s...

Let $\mathbf{F}_q$ be a finite field of $q$ elements. We show that the normalized Jacobi sum $q^{-(m-1)/2}J(\chi_1,\dots,\chi_m)$ ($\chi_1\dotsm \chi_m$ nontrivial) is asymptotically equidistributed on unit circle, when $\chi_1\in \mathcal{A}_1,\dots, \chi_m\in \mathcal{A}_m$ run through arbitrary sets nontrivial multiplicative characters $\mathbf{F}_q^\times$, if $\#\mathcal{A}_1\ge q^{\frac{1...

We study the transition between phases at large $R$-charge on a conformal manifold. These are characterized by behaviour of lowest operator dimension $\Delta(Q_R)$ for fixed and $Q_R$. focus, as an example, $D=3$, $\mathcal{N}=2$ Wess-Zumino model with cubic superpotential $W=XYZ+\frac{\tau}{6}(X^3+Y^3+Z^3)$, compute $\Delta(Q_R,\tau)$ using $\epsilon$-expansion in three interesting limits. In ...

We define interval valued (∈,∈∨q)-fuzzy k-ideals, interval valued (∈,∈∨q)-fuzzy k-quasi-ideals, interval valued (∈,∈∨q)-fuzzy k-bi-ideals and characterize k-regular and k-intra regular hemirings by the properties of interval valued (∈,∈∨q)-fuzzy k-ideals, interval valued (∈,∈∨q)-fuzzy k-quasi-ideals and interval valued (∈,∈∨q)-fuzzy k-bi-ideals. 2010 mathematics subject classification: 16Y60 • ...

Let $\epsilon>0$ and let $q$ be a prime going to infinity. We prove that with high probability given $x,y$ in the projective plane over finite field $F_q$ there exists $\gamma$ $SL_3(Z)$, coordinates bounded by $q^{1/3+\epsilon}$, whose projection $SL_{3}(F_q)$ sends $x$ $y$. The exponent $1/3$ is optimal result rank generalization of Sarnak's strong approximation theorem for $SL_2(Z)$.

We study the optical absorption, especially the (far-) infrared absorption by phonons, of semiconducting and metallic nanospheres. In the nanoscopic sphere, phonons as well as states of electronic excitations are quantized by confinement. It is also known that in the nanoscopic geometry, the confined electron-phonon interaction has a different form from the usual one in the bulk. First, we anal...

Let $\mathfrak{j}$ and $\mathfrak{j}^{'}$ be the Cartan subalgebras of complex semi-simple Lie algebras $\mathfrak{g}$ $\mathfrak{g}^{'}$, $\mathfrak{j}^{*}$ $(\mathfrak{j}^{'})^{*}$ their duals, $\mathfrak{j}^{\vee}$ $(\mathfrak{j}^{'})^{\vee}$ biduals respectively. We consider $B(.,.)$, restriction to Killing form $\mathfrak{g}^{'}$. In this work, using kernel $K$ reproducing subalgebra an op...

The definition of a D-admissible fuzzy subset for an operator domain D on a group G is modified to obtain new kinds of (∈,∈ ∨q)-fuzzy subgroups such as an (∈,∈ ∨q)-fuzzy normal subgroup, an (∈,∈ ∨q)-fuzzy characteristic subgroup, an (∈,∈ ∨q)fuzzy fully invariant subgroup which are invariant under D. As results, some of the fundamental properties of such (∈,∈ ∨q)−fuzzy subgroups are obtained.

Measles remains a major cause of child mortality, in part due to an inability to vaccinate young infants with the current live attenuated virus vaccine (LAV). To explore new approaches to infant vaccination, chimeric Venezuelan equine encephalitis/Sindbis virus (VEE/SIN) replicon particles were used to express the hemagglutinin (H) and fusion (F) proteins of measles virus (MV). Juvenile rhesus ...