A new multidimensional integral relationship between heat flux and temperature for direct internal assessment of heat flux

This paper derives a new integral relationship between heat flux and temperature in a transient, two-dimensional heat conducting half space. A unified mathematical treatment is proposed that is extendable to higher-dimensional and finite-region geometries. The analytic expression provides the local heat flux perpendicular to the front surface solely based on an embedded line of temperature sensors parallel to the surface. The relationship does not require apriori knowledge of the surface boundary condition. A new sensor strategy is analytically conceived based on the integral relationship for estimating the local, in-depth heat flux without surface instrumentation. It should further be clarified that the integral relationship requires only knowledge of the local, in-depth temperature and heating/cooling rate (time rate of change of temperature). The resulting formulation is mildly ill-posed and either requires digital filtering of the temperature signal to remove high frequency components of noise or the development of direct heating/cooling rate sensors. This paper (a) develops the new mathematical relationship; (b) demonstrates that the proposed relationship reduces to well-known (i) one-dimensional results under the appropriate assumptions; and, (ii) two-dimensional surface results; and, (c) provides a simple numerical example validating the concept.     

Spectrophotometric and spectrofluorimetric investigation of different equilibria of a recently synthesized Schiff base with the aid of chemometric methods

In this study ground and excited states acidic dissociation constants of a recently synthesized Schiff base was obtained in a DMF:water mixture of 30:70 (v/v) using absorption and fluorescent spectra of the Schiff base in different pH values with the aid of chemometric methods. In addition, the fluorescent of the two kinds of tautomers of this Schiff base was investigated and the rate of tautomerization was obtained using rank annihilation factor analysis (RAFA). The effect of different kinds of surfactants such as sodium dodecyl sulfate (SDS), cetyltrimethylammonium bromide (CTAB) and Triton X-100 on fluorescence spectrum of the Schiff base in a DMF:water mixture of 2:98 (v/v) was investigated. CTAB increased the fluorescence intensity of the Schiff base while SDS and Triton X-100 had no significant effect on it. β-Cyclodextrin increased the fluorescence intensity of the Schiff base. Also the sensing behavior of this Schiff base toward metal ions was studied in DMF and ethanol by fluorescence spectroscopy. The Schiff base showed prominent fluorescent signal in the presence of Zn²⁺, whereas other metal ions failed to induce response and ground-state dissociation constant of the complex was determined by direct fluorimetric titration as a function of Zn²⁺ concentration.     

Supported Preyssler Nanoparticles in Synthesis of 1,3‐Diaryl‐5‐Spirohexahydropyrimidines

Silica‐supported Preyssler nanoparticles (H₁₄[NaP₅W₃₀O₁₁₀])/SiO₂ are used as a new and recyclable catalyst for the preparation of 1,3‐diaryl‐5‐spirohexahydropyrimidines via a one‐pot condensation of anilines, formaldehyde, and cyclohexanone.     

Surprising Formation of Chlorinated Butenolides from Dialkyl Acetylenedicarboxylates and Hexachloro­acetone in the Presence of Triphenyl Phosphite

Triphenyl phosphite reacts smoothly with dialkyl acetylenedicarboxylates and hexachloroacetone to produce alkyl 2‐(dichloromethylene)‐2,5‐dihydro‐5‐oxo‐4‐(trichloromethyl)furan‐3‐carboxylates in good yields.     

A handy proof of Gay's theorem

In 1979, Gay proved that Broyden's methods, when used for n‐square linear systems, terminate in at most 2n iterations (SIAM J. Numer. Anal. 1979; 16 :623–630). Also, the ABS methods were introduced in 1984 (Numer. Math. 1984; 45 :1361–1376). In this paper we show another (handy) proof of Gay's theorem by these algorithms. Copyright © 2008 John Wiley & Sons, Ltd.     

Carbazolylmethylphosphonate compounds – Synthesis,coordination and fluorescence in solution and cells

The compounds diethyl-N-carbazolylmethylphosphonate 1 and diethyl-2-oxymethylphosphonate carbazole 2 have been synthesised and characterized by a range of techniques including NMR, absorption and emission spectroscopy, infrared, and mass spectroscopy. Compound 1 forms a 2:1 complex 3 with calcium nitrate and the single crystal X-ray diffraction structure of 3 is described. Titrations of 1 with Zn²⁺ and Ca²⁺ in ethanol reveal that the intrinsic fluorescence is only slightly perturbed in the presence of these metal ions in micromolar ethanol solutions. Compounds 1 and 2 are readily taken up and visualized in L929 fibrosarcoma and DRG (Dorsal root ganglia) cell lines.     

Quantum Spin Half Algebra and Generalized Megrelishvili Protocol for Confidentiality of Digital Images

International Journal of Theoretical Physics - Most of the enciphering structures are based on the transformation of mediums by describing the strict criteria. The presented article is based on...     

Pauli Half Spinning and Elliptic Curve Based Information Confidentiality Mechanism

International Journal of Theoretical Physics - The use of digital contents has increased tremendously in this modern era. In fact, people spend more time on internet than ever which urged the...     

Effect of quantization and positron concentration on shielding potentials in electron-positron-ion plasma

The kinetic theory of plasma has been employed to compute the test-charge potential distributions accounting for quantization effects in magnetized electron-positron-ion (EPI) plasmas. In this regard, the degenerate positrons and electrons are assumed to follow the Fermi-Dirac distribution, while inertial ions are modelled by Maxwellian velocity distribution. By solving the Fourier-transformed Vlasov–Poisson equations, a modified dielectric function and electrostatic potential is obtained. By imposing various constraints on the test-charge speed, the potential profile has been analysed in terms of Debye–Hückel (DH), far-field (FF), and wake-field (WF) potentials. It has been found that the amplitude of DH and FF potentials increases by the inclusion of quantization effects, and it becomes the opposite for the WF potential profile. Furthermore, the variation of positron concentration significantly affects the DH, FF, and WF potentials. The present findings are important to understand the shielding phenomenon in degenerate multi-species plasmas.     

Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

We have investigated the interaction of obliquely propagating ion acoustic solitary waves in a magnetoplasma with relativistically degenerate electrons. Using the quantum hydrodynamics model and by employing the extended Poincaré–Lighthill–Kuo technique, we have derived a set of Korteweg de Vries equations for two solitons. We have observed that the system under consideration allows the formation of only compressive solitons and their velocities remain in the sub-acoustic limit. Furthermore, phase shifts of solitons as a result of their interaction have been calculated. The phase shifts have been observed to be dependent on the obliqueness and the physical parameters of plasma. It has also been noticed that phase shifts remain negative for the whole range of parameters generally found in white dwarf stars. We have observed that the phase shifts enhance with the enhancement in number density, however, the converse happens when the magnetic field is enhanced. It has also been observed that the phase shift is slightly greater for the solitons that are less oblique as compared to their more oblique counterparts. Furthermore, we have estimated the spatial scales of interaction of solitons using the parameters found in white dwarf stars.