Search Results (36)

We consider the melting of a one-dimensional domain ($x\ge 0$), initially at the melting temperature $u=0$, by fixing the boundary temperature to a value $u(0,t)=U_0>0$—the so called Stefan melting problem. The governing transient heat-conduction equation involves a time derivative and the spatial derivative of the temperature gradient. In the general case the order of the time derivative and the gradient can take values in the range $(0,1]$. In these problems it is known that the advance of the melt front $s\left(t\right)$ can be uniquely determined by a specified prefactor multiplying a power of time related to the order of the fractional derivatives in the governing equation. For given fractional orders the value of the prefactor is the unique solution to a transcendental equation formed in terms of special functions. Here, our main purpose is to provide efficient numerical schemes with low computational complexity to compute these prefactors. The values of the prefactors are obtained through a dimensionalization that allows the recovery of the solution for the quasi-stationary case when the Stefan number approaches zero. The mathematical analysis of this convergence is given and provides consistency to the numerical results obtained. Full article

In this paper, it is proved that, for any sequence of positive numbers ${\xi }_n$, $n=1,2,\dots$, which does not converge to zero faster than the exponential function, and any sequence of positive numbers ${\delta }_n$, $n=1,2,3,\dots$, there is an uncountable set of positive numbers S such that, for each $\alpha >1$ in S, there are infinitely many $n\in \mathbb{N}$ for which the fractional parts $\left\{{\xi }_n{\alpha }^n\right\}$ are smaller than ${\delta }_n$, regardless of how fast the sequence ${\delta }_n$ tends to zero. In particular, for any sequence bounded away from zero, namely, ${\xi }_n\ge \xi >0$ for $n\ge 1$, it is shown that infinitely many integers n for which the inequality $\left\{{\xi }_n{\alpha }^n\right\}<{\delta }_n$ is true can be extracted from an arbitrary subsequence $\mathcal{N}$ of positive integers. Full article

Background/Objectives: Cardiovascular diseases are a leading cause of death, and psychosocial stress is considered a contributing factor to these issues. With the rising number of heart surgeries, proper rehabilitation post-surgery is essential. Previous studies have demonstrated the positive impact of yoga and transcendental meditation on the cardiovascular system. This pilot study aimed to investigate the effects of yoga and transcendental meditation on retinal microcirculation in cardiac patients before (admission), after (discharge), and following (3 weeks after discharge) rehabilitation. Methods: This study examined changes in retinal microcirculation in three rehabilitation groups of patients after heart surgery. The control group received standard exercise therapy, while the meditation group incorporated 20 min of meditation, and the yoga group incorporated 20 min of yoga practice, twice per day for the duration of four weeks of rehabilitation. Retinal images were captured using a non-mydriatic digital retinal camera (Canon CR-2, Canon Medical Systems Europe B.V., Netherlands), and the microcirculation parameters central retinal artery equivalent, central retinal vein equivalent, and artery-to-vein ratio were analyzed using MONA REVA software ((version 2.1.1), VITO, Mol, Belgium). Repeated measures ANOVA was performed to evaluate differences between the three groups in the course of rehabilitation. Results: None of the parameters revealed significant differences in retinal microcirculation between the three rehabilitation groups. Conclusions: The study evaluating changes in retinal microcirculation, as an indicator of central circulation in cardiac patients undergoing rehabilitation, did not observe any significant changes. As yoga and meditation are underestimated approaches in cardiac rehabilitation, this pilot study acts as a basis for providing preliminary information for future studies to encourage the research community to fill the gap in this area. Full article

Tomato (Solanum lycopersicum L.) is one of the most important cultivated vegetables in the world. However, in some countries such as Mexico the lack of cultivars adapted to different environmental production conditions is a limitation. Moreover, recent studies have indicated that breeding aimed at increasing yield has led to a loss of genetic diversity. Therefore, it is necessary to explore and characterize new sources of germplasms. This study aimed to characterize new sources of germplasm and identify the most transcendental traits for distinguishing tomato types and lines that are useful for the genetic improvement of the species. Sixty characters were evaluated in 16 advanced lines of native tomatoes from Central and Southern Mexico during the fall–winter cycles 2023–2024 at the Bajío Experimental Station, Celaya, Guanajuato, Mexico, based on the guidelines of the International Union for the Protection of New Varieties of Plants (UPOV) and the International Plant Genetic Resources Institute (IPGRI). The data were analyzed using descriptive statistics, analysis of variance and post hoc tests, canonical discriminant analysis, and the Eigenanalysis selection index method (ESIM). Morphological variation showed that five qualitative traits were determinant factors in distinguishing tomato types and lines, whereas agronomic discriminant traits were the equatorial and polar diameters of the fruit and its ratio, number of locules, pedicel length, stem length, and internode distance. In addition, significant positive correlations were found between leaf length and width, equatorial diameter of the fruit, and polar diameter of the fruit. Lines JCM-17, JMC-10, and JCM-01 were the most selectable lines according to the ESIM values. The morphological variation found and the characteristics with higher selection values identified may be valuable for optimizing the tomato genetic improvement process in general. Full article

This article presents a buck converter in which the inductor has been replaced by a transmission line. This approach would be practically conceivable if the power supply and load had a greater spatial distance. Alternatively, the model derived in this way could also be regarded as an intermediate model in order to replace a power coil via discretization with a larger number of smaller coils and capacitors. In the time domain, this new converter can be described by a system of coupled partial and ordinary differential equations. In the frequency domain, a transcendental transfer function is obtained. For comparison with an equivalently parameterized conventional converter, Padé approximants are derived. A linear controller is designed for the converter topology under consideration. Full article

The aim of this paper is to study the use of Lambert W functions in the analysis of nonlinear dynamics and bifurcations of a new two-dimensional $\gamma$-Ricker population model. Through the use of such transcendental functions, it is possible to study the fixed points and the respective eigenvalues of this exponential diffeomorphism as analytical expressions. Consequently, the maximum number of fixed points is proved, depending on whether the Allee effect parameter $\gamma$ is even or odd. In addition, the analysis of the bifurcation structure of this $\gamma$-Ricker diffeomorphism, also taking into account the parity of the Allee effect parameter, demonstrates the results established using the Lambert W functions. Numerical studies are included to illustrate the theoretical results. Full article

There is something queer about Symbolism. Art historians have long acknowledged the links between Symbolist aesthetics and contemporaneous ideas about human sexuality, and even a cursory examination of artworks by male Symbolist artists working across the continent reveals an eyebrow-raising number of muscled nudes, lithe ephebes, and intimate male couplings. The sensual male body could register the artist’s erotic desire, even as he put it forth as an idealized emblem of transcendental truth. But perhaps Symbolism’s queerness extended beyond subject matter. Scholars have argued that Symbolism was in part defined by a subversive approach to visual semiotics: a severing—we might say a queering—of the ties binding a sign to its established cultural meaning. Similarly, male homosexual subcultures were sustained by endowing established signs and pictures with a uniquely queer significance. This paper seeks to tease out the relationship between Symbolist aesthetics and male homosexuality in terms of a shared sensibility towards pictorial interpretation. Taking as a case study the work of the Swedish Symbolist artist Eugène Jansson, I argue that Symbolism held appeal for homosexual artists precisely because queer subcultures were primed to read subversive meaning into normative pictures. Offering a new reading of Symbolism’s sexual valences, I contextualize the movement’s attendant artworks within the broader cultural landscape of homosexual signs and symbols and articulate the parallels between Symbolist approaches to the image and queer modes of seeing in the late nineteenth century. Full article

The late Middle Ages witnessed a recapitulation of medieval reflection on beauty. Jean Gerson is an important representative of these philosophical and theological contributions, although he has been largely neglected up to this time. A first dimension of his ideas on beauty is the incorporation of beauty (pulchrum) into the number of transcendentals, i.e., the concepts “convertible” with the notion of being (ens), that is, unity, truth, and goodness (unum, verum and bonum). This article revisits Monica Calma’s study on Gerson’s theory of beauty and suggests new hypothetical sources that may have inspired this aspect of his thought. The second aspect emphasised here is Gerson’s classification of beauty, which entails some similarities to the one of Ulrich of Strasbourg, but also differs from it. Moreover, its incorporation of a division entirely devoted to artistic beauty is highly remarkable. Full article

Chaotic maps have been widely studied in the field of cryptography for their complex dynamics. However, chaos-based cryptosystems have not been widely used in practice. One important reason is that the following requirements of practical engineering applications are not taken into account: computational complexity and difficulty of hardware implementation. In this paper, based on the demand for information security applications, we modify the local structure of the three-dimensional Intertwining Logistic chaotic map to improve the efficiency of software calculation and reduce the cost of hardware implementation while maintaining the complex dynamic behavior of the original map. To achieve the goal by reducing the number of floating point operations, we design a mechanism that can be decomposed into two processes. One process is that the input parameters value of the original system is fixed to $2^k$ by Scale index analysis. The other process is that the transcendental function of the original system is replaced by a nonlinear polynomial. We named the new map as “Simple intertwining logistic”. The basic chaotic dynamic behavior of the new system for controlling parameter is qualitatively analyzed by bifurcation diagram and Lyapunov exponent; the non-periodicity of the sequence generated by the new system is quantitatively evaluated by using Scale index technique based on continuous wavelet change. Fuzzy entropy (FuzzyEn) is used to evaluate the randomness of the new system in different finite precision digital systems. The analysis and evaluation results show that the optimized map could achieve the designed target. Then, a novel scheme for generating pseudo-random numbers is proposed based on new map. To ensure its usability in cryptographic applications, a series of analysis are carried out. They mainly include key space analysis, recurrence plots analysis, correlation analysis, information entropy, statistical complexity measure, and performance speed. The statistical properties of the proposed pseudo random number generator (PRNG) are tested with NIST SP800-22 and DIEHARD. The obtained results of analyzing and statistical software testing shows that, the proposed PRNG passed all these tests and have good randomness. In particular, the speed of generating random numbers is extremely rapid compared with existing chaotic PRNGs. Compared to the original chaotic map (using the same scheme of random number generation), the speed is increased by 1.5 times. Thus, the proposed PRNG can be used in the information security. Full article

This paper considers polynomial characteristics useful for a better understanding of the behaviour of these functions. Taylor series for the polynomials are described by the items with even and odd derivatives and powered changes in the argument, which leads to more specific studying of their properties. Connections between the derivative and antiderivative of the polynomial functions are defined. The structure of polynomial functions reveals their specific characteristic that the mean value of their roots equals the mean value of the locations of the critical points such as the extrema and inflection points. Derivatives of the quadratic exponent in relation to an interesting connection of two transcendental numbers are also described. The discussed properties of the polynomials can be helpful for practical implementations and educational purposes. Full article

The rhythmic and stable operation of trolleybuses and autonomous trolleybuses or urban electric buses, depends to a large extent on the reliability of the equipment installed on the trolleybus. The actual operational reliability of trolleybus electrical equipment (EE) depends on its technical condition. Under the influence of external factors and specific operating modes, the technical condition of the equipment is continuously deteriorating, reliability indicators are decreasing, and the number of failures is increasing. Using the mathematical theory of reliability, probability theory and mathematical statistics, numerical methods of solving nonlinear and transcendental equations, this article defines the conditions of diagnostics depending on the intensity of failures and the given probability of failure-free operation of the equipment. Additionally, the inverse problem of determining the current reliability of electrical engineering systems depends on the terms of diagnostics and the intensity of failures being solved. As a result of the processing of statistical information on failures it is established that for the electrical equipment of a trolleybus, after a number of repair measures, the maximum density of failures occurs at a lower mileage, and the probability of failure-free operation can vary depending on the degree of wear of the equipment, i.e., on the number of previous failures. It is theoretically substantiated and experimentally confirmed that the reliability of trolleybus electrical equipment changes according to the exponential law of distribution of a random variable. It has been established that the real averaged diagnostic terms regulated by instructions are not optimal in most cases and differ several times from those defined in this paper. The dependence of switching equipment run-in on time has been clarified, which served as a prerequisite for specifying the inter-repair period for various types of trolleybus electrical equipment. A method of adjustment of the inter-repair time for the electrical equipment of trolleybuses is proposed. Full article

The well-known power-law fractal element was determined to need several important revisions by the authors of this work. It is now possible to demonstrate that any scaling equation associated with a fractal element is actually K-fold degenerated and includes previously unknown but crucial adjustments. These new discoveries have the potential to significantly alter the preexisting theory and create new connections between it and its experimental support, particularly when it comes to measurements of the impedances of diverse metamaterials. It is now easy to demonstrate that any random curve with a clearly stated tendency in a specific range of scales is self-similar using the method involving reduction to three invariant points (Ymx, Ymn, and Ymin). This useful procedure indicates that the chosen random curve, even after being compressed a certain number of times, still resembles the original curve. Based on this common peculiarity, it is now possible to derive “a universal” fitting function that can be used in a variety of applied sciences, particularly those that deal with complex systems, to parametrize many initial curves when a model fitting function derived from a simple model is not present. This self-similarity principle-derived function demonstrates its effectiveness in data linked to photodiode noise and the smoothed integral curves produced from well-known transcendental numbers E and Pi, which are considered in the paper as an example. Full article

In this study, a new switched-capacitor-based seven-level inverter topology with a photovoltaic system is presented. The proposed topology requires a smaller number of devices and has the ability to self-balance the voltage across the capacitor. The proposed topology configuration is simple and has the ability to extend to higher levels of voltage. This multilevel inverter topology is suitable for low- and medium-voltage applications with photovoltaic (PV) system integration. To improve the PV system efficiency as an input of a DC–DC boost converter, a Fuzzy logic-based maximum power point controller technique is used. A PV system with a DC–DC boost converter integrates with the proposed seven-level inverter topology. The anti-predatory particle swarm optimization (APSO) technique is used to solve the non-linear transduction equations of the seven-level PV switched-capacitor-based multilevel inverter (7L−PV−SCMLI) topology. The proposed APSO is described to minimize the harmonics in the multilevel inverter (MLIs), which is a complex optimization problem involving a non-linear transcendental equation. Furthermore, APSO can be applied in order to solve non-linear transcendental equations for all symmetrical and asymmetrical MLIs that have equal and non-equal DC sources. The APSO-based selected harmonic elimination (SHE) technique obtained the best switching angle value, and the optimized obtained switching angles reduced the total harmonic distortion (THD) of 7L−PV−SCMLI. Full article

The solution of the eigenvalue problem in bounded domains with planar and cylindrical stratification is a necessary preliminary task for the construction of modal solutions to canonical problems with discontinuities. The computation of the complex eigenvalue spectrum must be very accurate since losing or misplacing one of the thereto linked modes will have an important impact on the field solution. The approach followed in a number of previous works is to construct the corresponding transcendental equation and locate its roots in the complex plane using the Newton–Raphson method or Cauchy-integral-based techniques. Nevertheless, this approach is cumbersome, and its numerical stability decreases dramatically with the number of layers. An alternative, approach consists in the numerical evaluation of the matrix eigenvalues for the weak formulation for the respective 1D Sturm–Liouville problem using linear algebra tools. An arbitrary number of layers can thus be easily and robustly treated, with continuous material gradients being a limiting case. Although this approach is often used in high frequency studies involving wave propagation, this is the first time that has been used for the induction problem arising in an eddy current inspection situation. The developed method is implemented in Matlab and is used to deal with the following problems: magnetic material with a hole, a magnetic cylinder, and a magnetic ring. In all the conducted tests, the results are obtained in a very short time, without missing a single eigenvalue. Full article

Background: Cardiovascular diseases are the world’s number one cause of death, with exceeding psychosocial stress load being considered a major risk factor. A stress management technique that has repeatedly shown positive effects on the cardiovascular system is the Transcendental Meditation (TM) technique. The present pilot study aimed to investigate the potential effect of TM on the recovery of cardiac patients. Objectives: We hypothesized that practicing TM in patients undergoing a 4-week cardiac rehabilitation program augments the recovery of cardiovascular parameters and reduces skeletal muscle tone after rehabilitation. Methods: Twenty cardiac patients were recruited and randomly assigned to either the control or the TM group. Cardiovascular parameters were assessed with the Task Force Monitor (TFM) and skeletal muscle contractile properties by Tensiomyography during a sit-stand test, performed at the beginning and end of a 4-week in-patient rehabilitation program. Results: Systolic blood pressure (SBP) was significantly lower after 4 weeks of cardiac rehabilitation, while the RR-interval (RRI) significantly increased. At the skeletal muscle level, the contraction time and maximal displacement increased, though only in the gastrocnemius medialis and biceps femoris muscles and not in vastus lateralis. Group interactions were not observed for hemodynamic parameters nor for muscle contractile properties. Discussion: Although significant improvements in hemodynamic and muscular parameters were observed after 4 weeks of rehabilitation, we could not provide evidence that TM improved rehabilitation after 4 weeks. TM may unfold its effects on the cardiovascular system in the longer term. Hence, future studies should comprise a long-term follow-up. Full article