Comments on “arithmetic coding as a non-linear dynamical system”

Nagaraj et al. [1], [2] present a skewed-non-linear generalized Luroth Series (s-nGLS) framework. S-nGLS uses non-linear maps for GLS to introduce a security parameter a which is used to build a keyspace for image or data encryption. The map introduces non-linearity to the system to add an “encryption key parameter”. The skew is added to achieve optimal compression efficiency. s-nGLS used as such for joint encryption and compression is a weak candidate, as explained in this communication. First, we show how the framework is vulnerable to known plaintext based attacks and that a key of size 256 bits can be broken within 1000 trials. Next, we demonstrate that the proposed non-linearity exponentially increases the hardware complexity of design. We also discover that s-nGlS cannot be implemented as such for large bitstreams. Finally, we demonstrate how correlation of key parameter with compression performance leads to further key vulnerabilities.     

Tetranuclear Cu(II) complex supported by a central mu4-1,1,3,3 azide bridge

The new cluster [Cu4L2(N3)]Cl.16H2O has been synthesized and characterized; it features a unique mu4-1,1,3,3 bridging mode for azide, whose capacity to mediate magnetic coupling has been examined through bulk magnetic measurements and numeric fitting procedures.     

A linear worst-case lower bound on the number of holes inside regions visible due to multiple diffuse reflections

It is known that the region V(s) of a simple polygon P, directly visible (illuminable) from an internal point s, is simply connected. Aronov et al. [2] established that the region V₁(s) of a simple polygon visible from an internal point s due to at most one diffuse reflection on the boundary of the polygon P, is also simply connected. In this paper we establish that the region V₂(s), visible from s due to at most two diffuse reflections may be multiply connected; we demonstrate the construction of an n-sided simple polygon with a point s inside it so that the region of P visible from s after at most two diffuse reflections is multiply connected. We also show that V₃(s), the region of P visible from s after at most three diffuse reflections, can have (n) holes.A part of this work was done when this author was visiting the University of Miami, Coral Gables, Florida, USA.     

Bacteriocin PJ4 Active Against Enteric Pathogen Produced by Lactobacillus helveticus PJ4 Isolated from Gut Microflora of Wistar Rat (Rattus norvegicus): Partial Purification and Characterization of Bacteriocin

The increase of multidrug-resistant pathogens and the restriction on the use antibiotics due to its side effects have drawn attention to the search for possible alternatives. Bacteriocins are small antimicrobial peptides produced by numerous bacteria. Much interest has been focused on bacteriocins because they exhibit inhibitory activity against pathogens. Lactic acid bacteria possess the ability to synthesize antimicrobial compounds (like bacteriocin) during their growth. In this study, an antibacterial substance (bacteriocin PJ4) produced by Lactobacillus helveticus PJ4, isolated from rat gut microflora, was identified as bacteriocin. It was effective against wide assay of both Gram-positive and Gram-negative bacteria involved in various diseases, including Escherichia coli, Bacillus subtilis, Pseudomonas aeruginosa, Enterococcus faecalis, and Staphylococcus aureus. The antimicrobial peptide was relatively heat-resistant and also active over a wide pH range of 2–10. It has been partially purified to homogeneity using ammonium sulfate precipitation and size exclusion chromatography and checked on reverse-phase high-performance liquid chromatography. Sodium dodecyl sulfate–polyacrylamide gel electrophoresis of bacteriocin PJ4 purified through size exclusion chromatography resolved ~6.5 kDa protein with bacteriocin activity. The peptide is inactivated by proteolytic enzymes, trypsin, and lipase but not when treated with catalase, α-amylase, and pepsin. It showed a bactericidal mode of action against the indicator strains E. coli MTCC443, Lactobacillus casei MTCC1423, and E. faecalis DT48. Such characteristics indicate that this bacteriocin may be a potential candidate for alternative agents to control important pathogens.     

An Efficient Approximation Technique for Solving a Class of Fractional Optimal Control Problems

In this paper, we discuss a class of fractional optimal control problems, where the system dynamical constraint comprises a combination of classical and fractional derivatives. The necessary optimality conditions are derived and shown that the conditions are sufficient under certain assumptions. Additionally, we design a well-organized algorithm to obtain the numerical solution of the proposed problem by exercising Laguerre polynomials. The key motive associated with the present approach is to convert the concerned fractional optimal control problem to an equivalent standard quadratic programming problem with linear equality constraints. Given examples illustrate the computational technique of the method together with its efficiency and accuracy. Graphical representations are provided to analyze the performance of the state and control variables for distinct prescribed fractions.     

Duality for multiobjective fractional control problems with generalized invexity

Wolfe and Mond-Weir type duals for multiobjective control problems are formulated. Under pseudo-invexity/quasi-invexity assumptions on the functions involved, weak and strong duality theorems are proved to relate efficient solutions of the primal and dual problems.     

Regularized gap function as penalty term for constrained minimization problems

By using the regularized gap function for variational inequalities, Li and Peng introduced a new penalty function Pα(x) for the problem of minimizing a twice continuously differentiable function in closed convex subset of the n-dimensional space Rn. Under certain assumptions, they proved that the original constrained minimization problem is equivalent to unconstrained minimization of Pα(x). The main purpose of this paper is to give an in-depth study of those properties of the objective function that can be extended from the feasible set to the whole Rn by Pα(x). For example, it is proved that the objective function has bounded level sets (or is strongly coercive) on the feasible set if and only if Pα(x) has bounded level sets (or is strongly coercive) on Rn. However, the convexity of the objective function does not imply the convexity of Pα(x) when the objective function is not quadratic, no matter how small α is. Instead, the convexity of the objective function on the feasible set only implies the invexity of Pα(x) on Rn. Moreover, a characterization for the invexity of Pα(x) is also given.