Double Vivaldi antenna for wireless optical networks on chip

In this paper we present a double plasmonic Vivaldi antenna for on-chip optical wireless communication. The proposed antenna is a two-element broadside array fed by a silicon waveguide. The designs of the power splitter and of the hybrid Si-plasmonic coupler used for antenna excitation are described in detail. The array radiation characteristics are optimized through Finite Difference Time Domain simulations and the performance of a point-to-point link is evaluated. The proposed double Vivaldi array increases the gain of 3 dB with respect to a single antenna, improving the received power on a link of 6 dB when the double antenna is used for both transmitting and receiving sections.     

Macrocyclic depolymerization of arylene-ethynylene copolymers: a dynamic combinatorial method

A dynamic combinatorial approach for the synthesis of arylene ethynylene macrocycles (AEMs) from linear polymers is described. By using readily available carbazolyl-ethynylene copolymers as starting materials we obtained a number of novel macrocycles that would be difficult to prepare by traditional methods.     

Single-step fabrication of patterned gold film array by an engineered multi-functional peptide

This study constitutes a demonstration of the biological route to controlled nano-fabrication via modular multi-functional inorganic-binding peptides. Specifically, we use gold- and silica-binding peptide sequences, fused into a single molecule via a structural peptide spacer, to assemble pre-synthesized gold nanoparticles on silica surface, as well as to synthesize nanometallic particles in situ on the peptide-patterned regions. The resulting film-like gold nanoparticle arrays with controlled spatial organization are characterized by various microscopy and spectroscopy techniques. The described bio-enabled, single-step synthetic process offers many advantages over conventional approaches for surface modifications, self-assembly and device fabrication due to the peptides' modularity, inherent biocompatibility, material specificity and catalytic activity in aqueous environments. Our results showcase the potential of artificially-derived peptides to play a key role in simplifying the assembly and synthesis of multi-material nano-systems in environmentally benign processes.     

Mixed convexity and optimization results for an (S ? 1, S) inventory model under a time limit on backorders

Das (Oper Res 25(5):835–850, 1977) considered the optimization of a cost function associated with an (S ? 1, S) inventory model assuming the parameters to be the initial number of items in the stock and the service rate. A similar optimization problem associated with an M/E _k /1 queueing system with parameters being the number of servers and the service rate was considered by Kumin (Manag Sci 20:126–129, 1973). Both carried out case-dependent computations and indicated the difficulty of finding general convexity and optimization results for functions with both integer and real variables. In this paper, generalized mixed convexity and computational optimization results for the cost function associated with the (S ? 1, S) inventory system suggested by Das are provided. The generalized convexity results determine the convexity region of the cost function, and therefore the region of possible minimal values of the cost function in the domain. In addition, algorithms to determine the generalized convexity and computational optimization results for the cost function are given.     

B-free numbers in short arithmetic progressions

Given a sequence B of relatively prime positive integers with the sum of inverses finite, we investigate the problem of finding B-free numbers in short arithmetic progressions.     

Davenport constant for finite abelian groups

For a finite abelian group G, we investigate the length of a sequence of elements of G that is guaranteed to have a subsequence with product identity of G. In particular, we obtain a bound on the length which takes into account the repetitions of elements of the sequence, the rank and the invariant factors of G. Consequently, we see that there are plenty of such sequences whose length could be much shorter than the best known upper bound for the Davenport constant of G, which is the least integer s such that any sequence of length s in G necessarily contains a subsequence with product identity. We also show that the Davenport constant for the multiplicative group of reduced residue classes modulo n is comparatively large with respect to the order of the group, which is φ(n),when n is in certain thin subsets of positive integers. This is done by studying the Carmichael’s lambda function, defined as the maximal multiplicative order of any reduced residue modulo n, along these subsets.     

Synthesis and Characterization of Chloralose-Derived Thiosemicarbazones and Semicarbazones and Investigation of Their Antimicrobial Properties

Thiosemicarbazones(7–10)/semicarbazones(11–14) were synthesized in good yields via the condensation of α-gluco-, β-gluco-, galacto-, manno- chloralose derived 1,4-furanodialdoses (1-4) with thiosemicarbazide(5)/semicarbazide(6). The structures of all products were characterized by FTIR, NMR spectroscopic methods and elemental analysis. The compounds have been found to display moderate antimicrobial activity against Gram-positive, Gram-negative bacteria and antifungal activity against a Candida albicans. MIC values of the compounds range from 260 to 1510 μg/mL.     

A contemporary linear representation theory for ordinary differential equations: probabilistic evolutions and related approximants for unidimensional autonomous systems

In this paper, we build on our previous research on probabilistic foundations of dynamical systems and introduce a theory of linear representation for ordinary differential equations. The theory is developed for explicit ODEs and can be further extended to cover implicit cases. In this report, we investigate the case of a canonical single unknown autonomous system. First we construct a linear representation to get an infinite linear ODE set with a constant coefficient matrix which can be transformed into an upper triangular form. Then we find its approximate truncated solutions. We describe a number of properties of the theory using this framework. The companion of this paper expands this canonical approach to cover multidimensional cases using the theory of folded arrays which is another line of research established by our research group.