A remark on control of partially observed Markov chains

A new state variable is introduced for the problem of controlling a Markov chain under partial observations, which, under a suitably altered probability measure, has a simple evolution.     

On odd order nilpotent groups with class 2

Let G be an odd order nilpotent group with class 2 and let e denote the exponent of its commutator subgroup. Let ${e=p_1^{r_1}p_2^{r_2}\ldots p_s^{r_s}}Let G be an odd order nilpotent group with class 2 and let e denote the exponent of its commutator subgroup. Let e=p₁^r₁p₂^r₂?p_s^r_s{e=p_1^{r_1}p_2^{r_2}\ldots p_s^{r_s}}, where the p _i ’s are the prime divisors of the order of G and the r _i ’s are non-negative integers. Then there are at least (?_i=1^s(1+r_i))-1{\left(\prod_{i=1}^{s}(1+r_i)\right)-1} non-isomorphic nilpotent groups with class 2 and each of the groups has the same order structure as G.     

Character average of fourth power of Dirichlet L-series at unity

For a Dirichlet character modulo an integer \(q\ge 3\), we use a highly simple elementary method to give an asymptotic formula for \(\sum _{\chi \ne \chi _0 ({\bmod q})} {|L(1, \chi )|^{4}} ,\) where \(\chi _0 ({\bmod \, q})\) is the principal character. This result seems to be new.     

Effect of distortion on optical-fiber waveguides

We analyze the modes and coupling efficiency of asymmetric optical-fiber waveguides. We treated the step index-asymmetric optical-fiber waveguide as a boundary-value problem and obtain the expressions for the modes under logical assumptions. Using these expressions, we describe the propagation constants, mode delay, and power distribution of two asymmetric optical-fiber waveguides under consideration. Based on the perturbation theory, we also present the coupling coefficients of these asymmetric optical-fiber waveguides. We show that the waveguide parameters are considerably changed in the presence of distortion, and one can tune these parameters at the desired level by choosing suitable distortions.     

Prediction of extrudate swell in polymer melt extrusion using an Arbitrary Lagrangian Eulerian (ALE) based finite element method

Accurate prediction of extrudate (die) swell in polymer melt extrusion is important as this helps in appropriate die design for profile extrusion applications. Extrudate swell prediction has shown significant difficulties due to two key reasons. The first is the appropriate representation of the constitutive behavior of the polymer melt. The second is regarding the simulation of the free surface, which requires special techniques in the traditionally used Eulerian framework. In this paper we propose a method for simulation of extrudate swell using an Arbitrary Lagrangian Eulerian (ALE) technique based finite element formulation. The ALE technique provides advantages of both Lagrangian and Eulerian frameworks by allowing the computational mesh to move in an arbitrary manner, independent of the material motion. In the present method, a fractional-step ALE technique is employed in which the Lagrangian phase of material motion and convection arising out of mesh motion are decoupled. In the first step, the relevant flow and constitutive equations are solved in Lagrangian framework. The simpler representation of polymer constitutive equations in a Lagrangian framework avoids the difficulties associated with convective terms thereby resulting in a robust numerical formulation besides allowing for natural evolution of the free surface with the flow. In the second step, mesh is moved in ALE mode and the associated convection of the variables due to relative motion of the mesh is performed using a Godunov type scheme. While the mesh is fixed in space in the die region, the nodal points of the mesh on the extrudate free surface are allowed to move normal to flow direction with special rules to facilitate the simulation of swell. A differential exponential Phan Thien Tanner (PTT) model is used to represent the constitutive behavior of the melt. Using this method we simulate extrudate swell in planar and axisymmetric extrusion with abrupt contraction ahead of the die exit. This geometry allows the extrudate to have significant memory for shorter die lengths and acts as a good test for swell predictions. We demonstrate that our predictions of extrudate swell match well with reported experimental and numerical simulations.     

A solid-phase synthetic strategy for labeled peptides: synthesis of a biotinylated derivative of the delta opioid receptor antagonist TIPP (Tyr-Tic-Phe-Phe-OH)

A general solid-phase synthetic strategy for labeled peptides was developed and used to prepare a biotinylated derivative of the delta opioid receptor antagonist TIPP (Tyr-Tic-Phe-Phe-OH). A monoprotected hydrophilic diamine linker was attached to an aldehyde-containing solid-phase resin by reductive amination, followed by introduction of biotin and peptide synthesis to yield Tyr-Tic-Phe-Phe-Asp-NH(CH(2)CH(2)O)(2)CH(2)CH(2)NH-biotin (2). The high delta receptor affinity and selectivity of 2 demonstrate the applicability of this design approach for labeled peptide derivatives.     

Enrichment of Zinc and Iron Micronutrients in Lentil (Lens culinaris Medik.) through Biofortification

Biofortification of pulse crops with Zn and Fe is a viable approach to combat their widespread deficiencies in humans. Lentil (Lens culinaris Medik.) is a widely consumed edible crop possessing a high level of Zn and Fe micronutrients. Thus, the present study was conducted to examine the influence of foliar application of Zn and Fe on productivity, concentration, uptake and the economics of lentil cultivation (LL 931). For this, different treatment combinations of ZnSO₄·7H₂O (0.5%) and FeSO₄·7H₂O (0.5%), along with the recommended dose of fertilizer (RDF), were applied to the lentil. The results of study reported that the combined foliar application of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at pre-flowering (S1) and pod formation (S2) stages was most effective in enhancing grain and straw yield, Zn and Fe concentration, and uptake. However, the outcome of this treatment was statistically on par with the results obtained under the treatment ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage. A single spray of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage enhanced the grain and straw yield up to 39.6% and 51.8%, respectively. Similarly, Zn and Fe concentrations showed enhancement in grain (10.9% and 20.4%, respectively) and straw (27.5% and 27.6% respectively) of the lentil. The increase in Zn and Fe uptake by grain was 54.8% and 68.0%, respectively, whereas uptake by straw was 93.6% and 93.7%, respectively. Also the benefit:cost was the highest (1.96) with application of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage. Conclusively, the combined use of ZnSO₄·7H₂O (0.5%) + FeSO₄·7H₂O (0.5%) at S1 stage can contribute significantly towards yield, Zn and Fe concentration, as well as uptake and the economic returns of lentil to remediate the Zn and Fe deficiency.     

An organocatalytic direct Mannich-cyclization cascade as [3+2] annulation: asymmetric synthesis of 2,3-substituted pyrrolidines

A new method for asymmetric synthesis of 2,3-substituted pyrrolidines from N-PMP aldimines and succinaldehyde via formal [3+2] cycloaddition is reported. This reaction involves proline catalyzed direct Mannich reaction and acid catalyzed reductive cyclization with high yields (up to 78%) and excellent enantioselectivities (up to >99%).     

Asymmetric synthesis of 6-(2′,3′,4′,5′,6′-pentafluorophenyl)-δ-lactones via “allyl”boranes: application for the synthesis of fluorinated analog of key pharmacophore of statin drugs

Asymmetric “allyl”boration of pentafluorobenzaldehyde with various α-pinene based “allyl”boranes provides homoallylic alcohols in high de and ee; the alcohols have been converted into δ-lactones via acryloylation, ring-closing metathesis and hydrogenation. Pentafluorophenyl analog of key pharmacophore of statin drugs has been synthesized using diastereoselective epoxidation and regioselective reduction as key steps.