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A series of supplementary services to solve communication problems between deaf-mute people and society could decrease the additional risk caused by communication impairments and break the boundaries between deaf-mute people and doctors/society. This scientific article will serve as the basis of a future application to ease the social and medical burden of hearing-impaired patients. The economic effect that the integration of deaf-mute people can have involves both decreasing the costs allocated to social and health services for this category of people, and increasing the contribution of each deaf-mute person by increasing his productivity as an employee at a company/institution.

In this article we investigate some Hessian type equations. Our main aim is to derive new maximum principles for some suitable P-functions, in the sense of L.E. Payne, that is for some appropriate functional combinations of $$${u(x)}$$$ and its derivatives, where $$${u(x)}$$$ is a solution of the given Hessian type equations. To find the most suitable P-functions, we first investigate the special case of a ball, where the solution of our Hessian equations is radial, since this case gives good hints on the best functional to be considered later, for general domains. Next, we construct some elliptic inequalities for the well-chosen P-functions and make use of the classical maximum principles to get our new maximum principles. Finally, we consider some overdetermined problems and show that they have solutions when the underlying domain has a certain shape (spherical or ellipsoidal).

Alzheimer�s is a progresive neurodegenerative disease that interferes with human cognitive ability, memory and behavior. The inhibition of acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) enzymes are major therapeutic routes for the treatment of Alzheimer disease. In the study, nevel bis-polymethylenquinoline-bis-carboxamides (3a-f) and bis-polymethylenquinoline-bis-carboxylic acids (5a-b) having as precursor benzidine, were obtained in good yields by Pfitzinger condensation reactions of bis-isatines with corresponding cyclanones. The compounds were characterized by elemental analysis, FT-IR, NMR and mass spectrometry. Furthermore, the compounds were subjected to molecular docking dynamics simulations to ascertain their potentials as inhibitors of acetylcholinesterase (AChE) and butyrylcholinesterase (BChE). Molecular docking simulations showed varied binding activities towards the two binding sites of acetylcholinesterase: 4EY7 and 1OCD, and human butyrylcholinesterase: 1P0I. Compounds 3e and 5b demostrated strong binding affinities with 1P0I, 1OCD and 4EY7 biotargets similar to the binding modes of donepezil and tacrine (co-crystallized inhibitors of acetylcholinesterase) and butyrate (co-crystallized inhibitors of butyrylcholinesterase).

The use of mechatronic components and the incorporation of additive manufacturing into the process of product development have grown in popularity over the past several years. The goal of the research conducted in this paper is to develop a prototype of a monomobile biped mechanical system and to optimize the printing parameters for the additive manufacturing stage. This paper presents the modelling of the components of a biped mechanical system and the simulation of their operation. The modelling step is followed by setting the printing parameters in the dedicated Z-Suite software and creating the G-code for the Zortrax M300 Plus additive manufacturing equipment. Lastly, the paper presents the connection of the sensors to the Plusivo board, the mounting procedure to the 3D printed parts that make up the biped mechanical system as well as the operation methodology of the sensors. The resulting prototype is then used to monitor parameters specific to the sensors used.

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.

Starting from the theories and studies on armed conflicts and in particular civil wars, and based on relevant figures, this paper presents a comprehensive analysis of the Syrian Civil War. The Syrian conflict developed into a civil war with a sectarian dimension and has lasted longer mostly because of major powers, as well as some Middle Eastern countries that were directly and actively involved in the conflict, supporting the government forces or rebel groups. According to the analysed data, the war deeply affected the Syrian economy and its citizens due to the loss of governmental control over oil fields, the destruction of infrastructure and households, and the great number of forcibly displaced people and casualties. At the same time, the Syrian Civil War created great opportunities for arms-producing companies to sell their products without cutting off profits. Thus, the conclusion is that there is no benefit to war except for those who profit of it, namely the countries as well as the arms manufacturers that use conflicts as a proxy to promote their interests.

As a continuation of research on 1-vinylazulenes synthesis, on their physico–chemical properties as well as on their use as colorimetric and electrochemical materials for the detection of heavy metals ions, new compounds, 4-(azulen-1-ylmethylene)-2-phenyloxazol-5(4H)-ones, are reported. The exceptional structure of azulene moiety with symmetrical electron distribution only with respect to the x-axis gives some special chemical and physical properties to compounds in which it is inserted. Various azulene-1-carbaldehydes and hippuric acids are condensed with good yields in Erlenmeyer—Plöchl reaction conditions. The obtained 1-vinylzulenes were characterized and their UV-Vis and NMR spectra were briefly discussed.

In this note we derive some maximum principle for an appropriate function involving u, Du and $$D^2 u$$ , where $$u=u(x)$$ is a convex solution to a Monge–Ampere equation in a plane domain.

In this paper we are dealing with two classes of mean curvature type problems that generalize the translating soliton problem. A first result proves that the solutions to these problems have unique interior critical points. Using this uniqueness result, we next derive a priori C 0 and C 1 estimates for the solutions to these problems, by means of some minimum principles for appropriate P -functions, in the sense of L. E. Payne.

For a bounded domain Ω ⊂ R N , N ≥ 2 , and a real number p > 1 , we denote by u p the p -torsion function on Ω , that is the solution of the torsional creep problem Δ p u = − 1 in Ω , u = 0 on ∂ Ω , where Δ p u ≔ d i v ( ∇ u p − 2 ∇ u ) is the p -Laplace operator. Our aim is to investigate some monotonicity properties for the p -torsional rigidity on Ω , defined as T p Ω ≔ ∫ Ω u p d x . More precisely, we first show that there exists T ∈ 0 , 1 such that for each open, bounded, convex domain Ω ⊂ R N , with smooth boundary and δ Ω ≤ T , where δ Ω represents the average integral on Ω of the distance function to the boundary of Ω , the function p → T p ; Ω ≔ Ω p − 1 T p Ω 1 − p is increasing on 1 , ∞ . Moreover, we also show that for any real number s > T , there exists an open, bounded, convex domain Ω ⊂ R N , with smooth boundary and δ Ω = s , such that the function p → T p ; Ω is not a monotone function of p ∈ ( 1 , ∞ ) . Finally, we use this result to get a new variational characterization of T ( p ; Ω ) , in the case when δ Ω is small enough.

This paper is concerned with a general class of quasilinear anisotropic equations. We first derive some maximum principles for two appropriate P-functions, in the sense of Payne (see the book of Sperb [18]). These maximum principles are then employed to obtain a Liouville-type result and a Serrin–Weinberger-type symmetry result.

In this paper we are dealing with entire solutions of a general class of anisotropic equations. Under some appropriate conditions on the data, we show that the corresponding equations cannot have non-trivial positive solutions bounded from above.

This paper is concerned with the low eigenvalues of closed surfaces in , of given measure, which are topologically equivalent to a sphere. Our aim is to obtain an isoprimetric inequality giving an upper bound for the product of the first three non-trivial eigenvalues of a convex closed surface topologically equivalent to a sphere. Moreover, we will also derive some lower bounds for the first non-trivial eigenvalue of the regular octahedron and icosahedron.

The paper is concerned with the behavior of a transformer used to supply the excitation from a power group. Waveforms from the transformer secondary winding were recorded and analyzed. Numerical simulations were performed in order to evaluate the performances of different solutions for the improvement of transformer operation by means of diminishing the current and voltage harmonics. Passive filtering and a solution with reactance coils are addressed.

The paper aims to analyze the effects introduced by additional equipment and consumers (AEC) over power quality indices in electric substations and general internal services from a Romanian power plant which uses solid fuel combustion. AEC includes asynchronous motors, rectifiers and frequency converters, introduced for environment protection. The measurement points are presented. Some of the most significant per phase power quality indices were computed. The acquired data revealed that the coupling of AEC resulted into a significant diminishing of the power factor, which fell under the neutral value (values around 0.76 were obtained). Theoretical hypothesis were proved by tests, because significant harmonic weights (introduced by the additional equipment) were revealed. Evaluations of harmonic weights were done considering long sets of data. Per harmonic order statistics were computed, revealing the dynamic character of the harmonic pollution and the most harmful harmonic orders.

This note is mainly devoted to the solvability of Monge-Ampere equation det ( D2u ) = 1, in a C2 bounded strictly convex domain Ω ⊂ R2, subject to a contact angle boundary condition. A necessary condition for the solvability of this problem, involving the maximal value of the curvature k (s) of ∂Ω and the contact angle, was derived by X.-N. Ma in [10], making use of a maximum principle for an appropriate P-function (see, also, J. Urbas [20], for a different proof). Our main goal here is to prove a complementary result. More precisely, we will derive a new necessary condition of solvability, involving the minimal value of the curvature k (s) of ∂Ω and the contact angle. The main ingredients of our proof are the derivation of a minimum principle for the P-function employed by X.-N. Ma in his proof, respectively the use of some computations in normal coordinates with respect to the boundary ∂Ω. Finally, a similar minimum principle will be employed to derive some isoperimetric estimates for the classical convex solution of Monge-Ampere equation, subject to the homogeneous Dirichlet boundary condition.

This paper deals with the eigenvalues of the Neumann Laplacian on simply-connected Lipschitz planar domains with some rotational symmetry. Our aim is to continue the investigations from Enache and Philippin [7] and derive new isoperimetric estimates for eigenvalues of higher order.

In this paper we are going to investigate a free boundary problem for a class of anisotropic equations on a multiply-connected domain Ω ⊂ R N , N ≥ 2. Our aim is to show that if the problem admits a solution in a suitable weak sense, then the underlying domain Ω is a Wulff shaped ring. This result represents the anisotropic extension of a result obtained by Payne and Philippin (1991) [13] . For the proof, we make use of a maximum principle for an appropriate P -function, a Rellich type identity, an anisotropic form of Minkowski inequality for convex sets and some geometric arguments involving the anisotropic mean curvatures of the free boundaries.

In this article we investigate a general class of Monge-Ampere equations in the plane, including the constant Gauss curvature equation. Our first aim is to prove some maximum and minimum principles for suitable $P$-functions, in the sense of L.E. Payne. Then, these new principles are employed to solve a general class of overdetermined Monge-Ampere problems and to investigate two boundary value problems for the constant Gauss curvature equation. More precisely, when the constant Gauss curvature equation is subject to the homogeneous Dirichlet boundary condition, we prove several isoperimetric inequalities, while when it is subject to the contact angle boundary condition, some necessary conditions of solvability, involving the curvature of the boundary of the underlying domain and the given contact angle, are derived.

In this note we derive a maximum principle for an appropriate functional combination of u ( x ) and | ∇ u | 2 , where u ( x ) is a strictly convex classical solution to a general class of Monge–Ampere equations. This maximum principle is then employed to establish some isoperimetric inequalities of interest in the theory of surfaces of constant Gauss curvature in R N + 1 .

In this article, we investigate a general class of fully nonlinear elliptic equations, including Weingarten equations. Our first aim is to construct a general elliptic inequality for an appropriate functional combination of u(x) and |∇u(x)|, i.e. a kind of P-function P(x), in the sense of L.E. Payne (see the book of Sperb [Sperb, Maximum Principles and Their Applications, Academic Press, New York, 1981]), where u(x) is a given solution of our class of fully nonlinear equations. From this inequality, making use of Hopf's first maximum principle, we derive a maximum principle for P(x), which extend some similar results obtained by Philippin and Safoui [Philippin and Safoui, Some maximum principles and symmetry results for a class of boundary value problems involving the Monge-Ampere equation, Math. Models Methods Appl. Sci. 11 (2001), pp. 1073–1080; Philippin and Safoui, Some applications of the maximum principle to a variety of fully nonlinear elliptic PDE's, Z. Angew. Math. Phys. 54 (2003), pp. 739–755], ...

This paper is concerned with the eigenvalues of the Neumann Laplacian on various classes of domains of given measure: simply-connected Lipschitz planar domains, n-sided planar polygons and smooth N-dimensional domains. In each case, we consider some quantities involving low eigenvalues of the Neumann Laplacian for which we obtain new inequalities. Moreover, we sharpen a universal bound derived by M. Ashbaugh and R. Benguria for sum of reciprocal of Neumann eigenvalues. Our investigations make use of some properties of conformal mappings, Bessel functions, symmetric domains or some isoperimetric inequalities for moments of inertia. Copyright © 2013 John Wiley & Sons, Ltd.

Worldwide spinal cord injury incidence is rising, due to spikes in traffic incidences, violence and an increase in ageing population, prone to injuries. To satisfy an expanding market, a wide variety of spinal implantable devices are available. The current study develops a new concept for a lumbar intervertebral disk implant which addresses the disadvantages of current commercialised devices. The proposed intervertebral disk implant concept limits the anatomical movements of the trunk, replicating the functions of a natural intervertebral disk. Three concept variations were designed and evaluated using FEA simulations for three main operating hypotheses: Compression of vertebrae in normal up-right position; Lifting weights at a correct and at an incorrect angle; Shock in the lumbar region. Von Misses stress, URES: Resultant Displacement and ESTRN: Equivalent Strain studies were used to evaluate the capability of the intervertebral disk implant concept to withstand the design load. Concept 3 failed URES and ESTRN simulations for the hypotheses which involved lifting weights and delivering a shock in the lumbar region. Simulation revealed optimum results for Concept 1, which was selected for further research.

Azo dyes with either one or two identical or different azulen-1-yl moieties attached to the structure -N2-C6H4-N2-C6H4-N2- were prepared, the phenylene ring being either 1,3-1′,3′ or 1,4-1′,4′ disubstituted. The syntheses were accomplished in good yields via mono or bis diazotization of the corresponding anilines followed by the coupling with unsubstituted or alkyl substituted azulenes in acetic/acetate medium. The recorded electronic spectra of the synthesized compounds were analyzed and were compared with those of related compounds. The isosbestic points resulting from protonation of the azo compounds enabled pKa values to be determined. From these pKa values it is apparent that all studied compounds are very weak bases. The high solvatochromic property of the compounds with para,para-substituted phenylene groups reflects the hyperpolarizability of these compounds.

In a quest for novel persistent free radicals, two products were obtained from the reaction between 1,1-diphenylhydrazine and 4-chloro-7-nitrobenzofurazan: the expected 1-(4nitrobenzofurazan-7-yl)-2,2-diphenyl-hydrazine 3 formed via an SNAr process, and the unexpected 4,7-benzofurazandione-(bis-1,1-diphenylhydrazone) 4 formed from 3 by a further ipso substitution and dehydrogenation. Oxidation of 3 with solid PbO2 or solid KMnO4 at room temperature affords during the first few minutes a persistent mono-nitro-hydrazyl free radical 6, which reacts with NO2 and forms another persistent hydrazyl free radical 7 having two nitro groups. Two blue dimeric compounds, 11 and 13, were obtained by dimerisation of 6 and 7 respectively, and loss of N2O4, and their structures were determined by mass spectrometry and NMR spectra. Additionally, single crystal X-ray diffraction was used to ascertain the structures of compounds 4 and 13. Other novel derivatives were prepared either by N-alkylation of 3 with General Papers ARKIVOC 2011 (xi) 198-221 Page 199 ARKAT-USA, Inc. methyl iodide, which afforded compound 5, or by homolytic nitration of 3 with gaseous NO2 which yielded the 4,7-dinitrobenzofurazan derivative 8. When gaseous NO2 was used in a similar reaction, only one N-nitro group was present in the product 7. Persistent free radicals were obtained from 4, 11, or 13 with KMnO4. Cyclic voltammograms for 3 and 8 as well as electronic absorption spectra for all new compounds 3, 4, 5, 8, 11, and 13 are discussed.

problem (¢u = 1 in ›, and u = 0 on @›) has a constant outward normal derivative on @›, is the N-dimensional ball. Serrin’s proof is based on the moving plane method and Hopf’s maximum principles. Under weaker assumptions on the regularity of @›, H.F. Weinberger presented in a subsequent paper [20] a simpler proof of Serrin’s basic result. His method of proof combines a maximum principle for a suitable P-function and a Rellich type identity resulting from Green’s theorem. However, Weinberger’s proof relies on the linearity of the Laplacian, while Serrin’s method could be extended to more general nonlinear elliptic equations.

Pyranylium perchlorates with azulen-1-yl moiety in 4-position and thiophen-2-yl or furan-2-yl in 2 and 6-positions were obtained by the substitution of 4-chloro corresponding salts with azulenes. The pyranylium salts are used as starting materials for the synthesis of pyridine and pyridinium salts. The products were characterized and for pyridines pKa was spectroscopically determined. Several attempts were made for pyridine complexation with metal cations as Hg2+ or Ag+. J. Heterocyclic Chem., (2011).

This paper deals with some non-linear initial-boundary value problems under homogeneous Neumann boundary conditions, in which the solutions may blow up in finite time. Using a first-order differential inequality technique, lower bounds for blow-up time are determined.

This paper is concerned with a class of boundary value problems for fully nonlinear elliptic PDEs involving the p-Hessian operator. We first derive a maximum principle for a suitable function involving the solution u(x) and its gradient. This maximum principle is then applied to obtain some sharp estimates for the solution and the magnitude of its gradient. We also investigate some symmetry properties of Ω or u(x) under specific boundary condition or geometry of Ω.

3- and 4-[(Azulen-1-yl)-azo]-azo-benzenes were obtained in good yields using the buffered coupling reaction between several alkyl-substituted azulenes and diazotized phenylazo-phenylamines in dichloroacetic acid. The coupling products were characterized and the recorded electronic spectra are discussed. The isosbestic points obtained by protonation enabled the determination of their p K a values.

This paper deals with a class of nonlinear parabolic problems in divergence form whose solutions, without appropriate data restrictions, might blow up at some finite time. The purpose of this paper is to establish conditions on the data sufficient to guarantee blow-up of solution at some finite time τ , conditions to ensure that the solution remains bounded as well as conditions to derive some explicit exponential decay bounds for the solution and its derivatives.

2-(Azulen-1-yl)-4,6-diphenyl substituted pyranylium salts, pyridinium salts and pyridines were efficiently synthesized and the new obtained compounds were completely characterized. Comparative structural analysis between these compounds and their corresponding isomers that contain the azulen-1-yl moiety in the 4-position of the heterocycle, were carried out. These studies are based on calculated dihedral angles formed between central heterocycle and the aromatic substituents and on the obtained electronic and NMR spectra. Due to the restriction in the rotation around azulenyl-pyridinium bond produced by the quaternary nitrogen substituent, in the herein reported pyridinium salts, the substitution groups of the quaternary nitrogen atom are prochiral. This property leads to the non-equivalence of gem-protons or gem-methyl groups of N-substituents in the 1H nmr spectra of the synthesized pyridinium salts.

New six unexpected 1,3,4-oxadiazoles were obtained starting from acylthiosemicarbazides. N1-[4-(4-X-phenylsulfonyl)benzoyl]-N4-(2/3-methoxyphenyl)-thiosemicarbazides 2,3a-c were treated with ethyl chloro- or bromoacetate in presence of anhydrous sodium acetate in order to obtain new thiazolidin-4-ones compounds. However, formation of desired thiazolidin-4-ones from these acylthiosemicarbazides failed and instead 1,3,4-oxadiazoles were obtained. For confirmation presence of these compounds, 5-[4-(phenylsulfonyl)phenyl]-2-(3-methoxyphenylamino)-1,3,4-oxadiazole 5a was synthetized by cyclodesulfurization of acylthiosemicarbazide 3a with mercury (II) acetate. The structures of these compounds were elucidated by FTIR, UV, 1H-NMR and 13C-NMR, MS spectra and elemental analysis.