On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

Dual sufficient characterizations of transversality properties

Positivity - This paper continues the study of ‘good arrangements’ of collections of sets near a point in their intersection. Our aim is to develop a general scheme for quantitative...     

Some results on linear nabla Riemann-Liouville fractional difference equations

In this paper, we establish some criteria for boundedness, stability properties, and separation of solutions of autonomous nonlinear nabla Riemann-Liouville scalar fractional difference equations. To derive these results, we prove the variation of constants formula for nabla Riemann-Liouville fractional difference equations.     

Self-adaptive gradient projection algorithms for variational inequalities involving non-Lipschitz continuous operators

Numerical Algorithms - In this paper, we introduce a self-adaptive inertial gradient projection algorithm for solving monotone or strongly pseudomonotone variational inequalities in real Hilbert...     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

Comparison of efficiency calibration techniques of HPGe detector for radioactivity measurement of soil sample in Marinelli geometry

Journal of Radioanalytical and Nuclear Chemistry - To keep the accredited category for the gamma spectrometry test in our laboratory, the efficiency curves of a HPGe detector for soil sample in...     

Type S Non-Ribosomal Peptide Synthetases for the Rapid Generation of Tailormade Peptide Libraries**

Bacterial natural products in general, and non-ribosomally synthesized peptides in particular, are structurally diverse and provide us with a broad range of pharmaceutically relevant bioactivities. Yet, traditional natural product research suffers from rediscovering the same scaffolds and has been stigmatized as inefficient, time-, labour- and cost-intensive. Combinatorial chemistry, on the other hand, can produce new molecules in greater numbers, cheaper and in less time than traditional natural product discovery, but also fails to meet current medical needs due to the limited biologically relevant chemical space that can be addressed. Consequently, methods for the high throughput generation of new natural products would offer a new approach to identifying novel bioactive chemical entities for the hit to lead phase of drug discovery programs. As a follow-up to our previously published proof-of-principle study on generating bipartite type S non-ribosomal peptide synthetases (NRPSs), we now envisaged the de novo generation of non-ribosomal peptides (NRPs) on an unreached scale. Using synthetic zippers, we split NRPSs in up to three subunits and rapidly generated different bi- and tripartite NRPS libraries to produce 49 peptides, peptide derivatives, and de novo peptides at good titres up to 145 mg L⁻¹. A further advantage of type S NRPSs not only is the possibility to easily expand the created libraries by re-using previously created type S NRPS, but that functions of individual domains as well as domain-domain interactions can be studied and assigned rapidly.     

One‐Step Pyro‐Synthesis of a Nanostructured Mn3O4/C Electrode with Long Cycle Stability for Rechargeable Lithium‐Ion Batteries

A nanostructured Mn₃O₄/C electrode was prepared by a one‐step polyol‐assisted pyro‐synthesis without any post‐heat treatments. The as‐prepared Mn₃O₄/C revealed nanostructured morphology comprised of secondary aggregates formed from carbon‐coated primary particles of average diameters ranging between 20 and 40 nm, as evidenced from the electron microscopy studies. The N₂ adsorption studies reveal a hierarchical porous feature in the nanostructured electrode. The nanostructured morphology appears to be related to the present rapid combustion strategy. The nanostructured porous Mn₃O₄/C electrode demonstrated impressive electrode properties with reversible capacities of 666 mAh g^?1 at a current density of 33 mA g^?1, good capacity retentions (1141 mAh g^?1 with 100 % Coulombic efficiencies at the 100^th cycle), and rate capabilities (307 and 202 mAh g^?1 at 528 and 1056 mA g^?1, respectively) when tested as an anode for lithium‐ion battery applications.