Constructive Solution of Inverse Parametric Linear/Quadratic Programming Problems

Parametric convex programming has received a lot of attention, since it has many applications in chemical engineering, control engineering, signal processing, etc. Further, inverse optimality plays an important role in many contexts, e.g., image processing, motion planning. This paper introduces a constructive solution of the inverse optimality problem for the class of continuous piecewise affine functions. The main idea is based on the convex lifting concept. Accordingly, an algorithm to construct convex liftings of a given convexly liftable partition will be put forward. Following this idea, an important result will be presented in this article: Any continuous piecewise affine function defined over a polytopic partition is the solution of a parametric linear/quadratic programming problem. Regarding linear optimal control, it will be shown that any continuous piecewise affine control law can be obtained via a linear optimal control problem with the control horizon at most equal to 2 prediction steps.     

Soliton collisions with wavelength-division multiplexed systems with strong dispersion management

We investigate collisions between solitons in a lossless two-channel wavelength-division multiplexed system with strong dispersion management. Numerical results show that the net frequency shift that is due to interchannel collisions is at least 1 order of magnitude smaller than predicted by adiabatic theories. A modified theoretical analysis is presented and shown to be in good agreement with the numerical results.     

Synthesis and Biological Evaluation of New N-Acyl-α-amino Ketones and 1,3-Oxazoles Derivatives

In order to develop novel bioactive substances with potent activities, some new valine-derived compounds incorporating a 4-(phenylsulfonyl)phenyl fragment, namely, acyclic precursors from N-acyl-α-amino acids and N-acyl-α-amino ketones classes, and heterocycles from the large family of 1,3-oxazole-based compounds, were synthesized. The structures of the new compounds were established using elemental analysis and spectral (UV-Vis, FT-IR, MS, NMR) data, and their purity was checked by reversed-phase HPLC. The newly synthesized compounds were evaluated for their antimicrobial and antibiofilm activities, for toxicity on D. magna, and by in silico studies regarding their potential mechanism of action and toxicity. The 2-aza-3-isopropyl-1-[4-(phenylsulfonyl)phenyl]-1,4-butanedione 4b bearing a p-tolyl group in 4-position exhibited the best antibacterial activity against the planktonic growth of both Gram-positive and Gram-negative strains, while the N-acyl-α-amino acid 2 and 1,3-oxazol-5(4H)-one 3 inhibited the Enterococcus faecium biofilms. Despite not all newly synthesized compounds showing significant biological activity, the general scaffold allows several future optimizations for obtaining better novel antimicrobial agents by the introduction of various substituents on the phenyl moiety at position 5 of the 1,3-oxazole nucleus.     

s-strongly perfect cartesian product of graphs

The study of perfectness, via the strong perfect graph conjecture, has given rise to numerous investigations concerning the structure of many particular classes of perfect graphs. In “Perfect Product Graphs” (Discrete Mathematics, Vol. 20, 1977, pp. 177--186), G. Ravindra and K. R. Parthasarathy tried, but unfortunately without success, to characterize the perfectness of the cartesian product of graphs (see also MR No. 58--10567, 1979). In this paper we completely characterize the graphs that are both nontrivial cartesian products and s-strongly perfect.     

Timing-jitter reduction in a fiber laser mode locked by an input bit stream

We present analytical and numerical results for the amount of timing-jitter reduction obtained in an all-optical clock-recovery device in which a data stream is used to mode lock a fiber laser through cross-phase modulation. This situation is analyzed when the laser pulses are close to optical solitons, so the effect of the data stream on the laser pulses is predicted from soliton perturbation theory. In our numerical simulations, both periodic input and pseudorandom input data streams are considered. The results show that for both types of data the rms timing jitter in the recovered clock is reduced significantly from that present in the input data.     

Soliton collisions in dispersion-managed wavelength-division-multiplexed systems

We show that collision-induced frequency shifts in wavelength-division-multiplexed (WDM) soliton transmission systems are strongly suppressed with increasing dispersion management. We predict new oscillations in the residual frequency shift response, owing to the relative motion induced by the dispersion map, and demonstrate a direct correlation between these oscillations and the modified soliton-collision dynamics. Simple analytical expressions for the oscillation minima are obtained, and implications for WDM soliton system design are discussed.     

Some fixed point results in $$\varvec{D^*}$$-quasimetric spaces

In this paper, we prove some coincidence and common fixed point theorems for self-maps satisfying contractive conditions in a \(D^*\)-quasimetric space.     

Development of finite-amplitude two-dimensional and three-dimensional disturbances in jet flows

The laminar-turbulent transition zone is investigated for a broad class of jet flows. The problem is considered in terms of the inviscid model. The solution of the initial-boundary value problem for three-dimensional unsteady Euler equations is found by the Bubnov-Galerkin method using the generalized Rayleigh approach [1–4]. The occurrence, subsequent nonlinear evolution and interaction of two-dimensional wave disturbances are studied, together with their secondary instability with respect to three-dimensional disturbances.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 8–19, September–October, 1985.