Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative an...
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Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.
The initial value problem for the quantum Zakharov equation in three di- mensions is studied. The existence and uniqueness of a global smooth solution are proven with coupled a priori estimates and the Galerkin method.
The initial value problem for the quantum Zakharov equation in three di- mensions is studied. The existence and uniqueness of a global smooth solution are proven with coupled a priori estimates and the Galerkin method.
A graph G is k-vertex-critical if χ(G) = k but χ(G − v) 1, H2)-free if it contains no induced subgraph isomorphic to H1 nor H2. A W4 is the graph consisting of a C4 plus an additional vertex adjacent to all the vert...
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We report enhanced accuracy in isotope-shift (IS) measurement using sympathetic cooling, demonstrated with Yb+170,172,174,176 transitions at 369 and 935 nm. Considering only type-A uncertainties, sympathetic cooling a...
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We report enhanced accuracy in isotope-shift (IS) measurement using sympathetic cooling, demonstrated with Yb+170,172,174,176 transitions at 369 and 935 nm. Considering only type-A uncertainties, sympathetic cooling achieves 30- and 200-fold improvements in IS measurement accuracy at 369 and 935 nm compared with previous single-ion results. Our measurements remain the most accurate to date including type-B uncertainties. King-plot analysis yields model-independent IS factors for these transitions [F369=−12.3(8) GHz/fm2, K369=−1800(1400) GHz u, F935=30.7(2.0) GHz/fm2, and K935=12900(3000) GHz u] and their ratio [F935F369=−2.498(4)] along with K935−K369F935F369=8410(90) GHz u, representing a 17-fold improvement. More reliable nuclear charge radii for Yb170–174,176 are also determined with an accuracy of 0.01 fm2. This paper complements collinear laser spectroscopy, introduces a robust approach for researching unstable isotopes, and supports applications of sympathetic cooling in trapped-ion quantum computers and quantum frequency standards.
Plant-based essential oils are complex natural products composed of volatile compounds with wide applications in food, cosmetics, and pharmaceuticals. Their bioactive properties, including antimicrobial, antioxidant, ...
Plant-based essential oils are complex natural products composed of volatile compounds with wide applications in food, cosmetics, and pharmaceuticals. Their bioactive properties, including antimicrobial, antioxidant, and anti-inflammatory effects, make them promising candidates for food flavoring, preservation, and therapeutic uses. Variations in chemical composition are influenced by geographical, climatic, and extraction factors, necessitating further investigation into their functional roles. This review aims to explore the versatile applications of plant-based essential oils, emphasizing their use in food flavoring, culinary practices, and health benefits. The paper highlights their potential as natural preservatives, flavor enhancers, and bioactive agents, while also addressing challenges such as toxicity, allergenicity, and interactions with food components. A comprehensive literature review was conducted to analyze studies on the extraction methods, chemical compositions, and biological activities of essential oils. Data was gathered to evaluate their antimicrobial, antioxidant, and preservative properties, along with their impact on food quality and safety. Essential oils exhibit significant antimicrobial and antioxidant activities, enabling their use as natural preservatives in food systems, active packaging, and edible coatings. Their incorporation into products such as cheese, ice cream, and beverages has demonstrated enhanced sensory attributes and prolonged shelf life. Encapsulation techniques have shown promise in minimizing interactions with food matrices, ensuring stability, and preserving bioactivity. Plant-based essential oils represent versatile natural additives with functional and sensory benefits. Their antimicrobial, antioxidant, and flavor-enhancing properties support their use in food preservation and flavoring. Encapsulation techniques effectively address challenges related to solubility and stability, enhancing their practical applications
We consider the FitzHugh-Nagumo system on undulated cylindrical surfaces modeling nerve axons. We show that for sufficiently small radii and for initial conditions close to radially symmetrical ones, (i) the solutions...
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It is presented in this paper that the new design and its analysis of finite difference domain decomposition algorithms for the two-dimensional heat equation, and the numerical results have shown the stability and acc...
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It is presented in this paper that the new design and its analysis of finite difference domain decomposition algorithms for the two-dimensional heat equation, and the numerical results have shown the stability and accuracy of the algorithms, where SauFyev asymmetric schemes have been used at the interface points. The Algorithm II in this paper has further extended those developed by Dawson and the others, Zhang and Shen.
We extend the celebrated Glivenko–Cantelli theorem, sometimes called the fundamental theorem of statistics, from its standard setting of total variation distance to all f-divergences. A key obstacle in this endeavor ...
Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipol...
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Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipolar drift-diffusion model. In addition, the authors also prove the existence of weak solution.
A discussion of the cross-spectral properties of eddies in the lowest 40 m of the nocturnal boundary layer is presented. The study involves the analysis of meteorological data collected by the British Antarctic Survey...
A discussion of the cross-spectral properties of eddies in the lowest 40 m of the nocturnal boundary layer is presented. The study involves the analysis of meteorological data collected by the British Antarctic Survey at Halley Station, Antarctica, during the austral winter of 1986. Cross-spectral analysis is used to determine whether the nature of the observed eddies is primarily turbulent or whether their structure is characteristic of coherent internal gravity waves. It is found that the cross-spectral phases indicate the presence of turbulent eddies only when the local gradient Richardson number (Ri) is less than the critical value of 1/4. Trapped modes were only observed when an offshore wind prevailed, indicating that topographic effects are responsible for their generation. The relative phases of velocity and temperature were often observed to change with height. This can be explained by examining the underlying meteorological conditions. On several occasions, regions of counter-gradient fluxes were detected. A physical explanation of this phenomenon is proposed.
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