Proceedings of the National Academy of Sciences, India Section A: Physical Sciences最新文献

In the present paper, we set forth with the new notion of rough (mathcal {I})-deferred statistical convergence of order (alpha (0<alpha le 1)) in gradual normed linear spaces (GNLS). We prove some fundamental features and implication relations of this convergence method. Also, we put forward the notion of gradual rough (mathcal {I})-deferred statistical limit set of order (alpha ) and prove some of its properties such as closedness and convexity. We prove that the gradual rough (mathcal {I})-deferred statistical limit set also plays a crucial role in the gradually (mathcal {I})-deferred statistical boundedness of order (alpha ) of a sequence in a GNLS. We end up proving a necessary and sufficient condition for the rough (mathcal {I})-deferred statistical convergence of order (alpha (0<alpha le 1)) of a sequence in GNLS. Significance of the work in a broad context: Summability theory and convergence of sequences have many applications in mathematical analysis. The study of the convergence of sequences in GNLS has made little progress and is still in its early stages. In this paper, we introduce rough (mathcal {I}-)deferred statistical convergence of sequences in GNLS which provides a new direction to the researchers.

Selenium has attracted considerable attention from different scientific communities since its discovery by Jöns Jacob Berzelius in 1817. Initial 150 years witnessed limited activities in selenium research which started expanding significantly after the 1970s. Today areas as diverse as physics, chemistry, biology, medicine, environment, food, agriculture, etc. are finding research problems related to selenium. This perspective aims to give a brief overview of the emerging trends in different areas of selenium research, particularly in biological and material sciences, which may hold major promise for the future. Relevance of organoselenium compounds in biological processes as well as in the development of advanced materials is covered.

The de novo programming technique is used to design an optimal system when the objectives and constraints are linear. It was initially introduced with crisp parameters. Later, de novo programming with fuzzy parameters has been studied to make it more flexible. But the fuzzy set has its limitations too. On the other hand, type-2 fuzzy sets are capable of embracing even those uncertainties that have not been covered or addressed by fuzzy sets. So the general de novo programming problem with interval type-2 fuzzy parameters has been introduced and studied here to make the system more reliable by removing the shortcomings of the human thinking process. This makes de novo programming better for modelling real-life problems than a fuzzy (type-1 fuzzy) logic-based system. The solution procedures for the proposed problem have been illustrated by a solid transportation problem.

The multiplicative first Zagreb index is discussed in this paper and studied for fuzzy graphs. Bounds of this index are calculated for path, cycle, star, complete fuzzy graph, partial fuzzy subgraph, etc. For an isomorphic fuzzy graph, it is shown that the value of this index is the same. Some interesting relations are established among the first Zagreb index, F-index and multiplicative first Zagreb index for a fuzzy graph. The bounds of this index are studied for some fuzzy graph operations. Also, the crime of kidnapping and abduction in metropolitan cities in India is analyzed by this index. Significant Statement: Topological indices for a crisp graph have applications in real life. But sometimes, it is seen that most real-life problems cannot be modeled using crisp graphs. Also, laboratory testing of chemicals to understand their different properties are costly. To overcome this, many topological indices have been presented in theoretical chemistry. Those topological indices are needed to define for a fuzzy graph for these circumstances.

Modern broadband and data communication systems strongly rely on the principles of orthogonal frequency division multiplexing (OFDM) for effective high speed data transfer between wireless systems and devices. But the underlying OFDM scheme has large peak to average power ratio (PAPR) value associated with it which can severely affect the overall system’s performance by degrading the bit error rate (BER) performance and increasing the out of band radiation. This article proposes a precoder-based partial transmit sequence (P-PTS) method in which the OFDM signal is precoded in order to reduce the out of band radiation and maintain the BER performance, while the PTS scheme is used to reduce the PAPR value. The effectiveness of P-PTS is validated for a 16 QAM modulated OFDM signal with 1024 subcarriers when transmitted over additive white Gaussian Noise (AWGN) channel and Rayleigh channel to the OFDM receiver section. The simulation analysis ensures that PAPR reduction is achieved by nearly 50% when compared to the original OFDM signal without degrading the BER performance.

In the present work, numerical investigation is carried out on the effect of dump gap and geometry in the performance characteristics of dump combustor diffuser. Dump gap ratio is the essential quantity that determines the losses and the radius of curvature of the flow at the exit plane. The effect of altitude on the pressure and temperature distributions of the dump diffuser is studied numerically through the SST k − ω turbulence model. A novel dome geometric shape optimization strategy is proposed adjacent to the flame tube head, and the effective flow pattern and pressure distribution caused by the dome shapes are analyzed using ANSYS. The dump gap ratio about 1.1 with optimized dome shapes offers better results as compared to the others in terms of static pressure recovery. The temperature and pressure distributions of the optimized geometry are validated with the existing state-of-the-art parametric studies, and the results are presented. Relevance of the work: the proposed numerical investigation on the influence of dump gap and flame tube geometry in the diffuser performance has several technical merits toward the core functions of a gas turbine engine specifically at high altitudes. The state-of-the-art pressure recovery retention mechanism can also be deployed for various physical flow environments to attain the specific values for the primitive variables as discussed in this article.

The solution to electromagnetic problems relies on complex numerical differential equations that are difficult to understand. Therefore, it is crucial to analyze them step by step and visualize them in a computer environment, even by developing a program. This approach enhances understanding of the subject and facilitates further research. In this study, an electromagnetic phenomenon is examined on a ferromagnetic structure using the Maxwell 2D static-elliptical partial differential equation within a developed software environment. The paper covers all aspects, ranging from the mathematical model and analysis solution to the fundamental operating parameters and characteristics, with a focus on educational purposes. The modeling and software development have been executed in a user-friendly manner, enabling students to apply various numerical techniques to practical problems while maintaining control over the entire modeling process. Through this study, it is anticipated that the transition from theory to practice can be facilitated more smoothly and directly. The theoretical analysis has been conducted using Mathematica software, and a comparison with finite element magnetic method simulation on a typical magnetic structure has been presented to illustrate the analogy. A comprehensive analysis of the Maxwell static-elliptical electromagnetic equation, based on a 2D numerical solution within a specific domain, has been performed in a detailed and unambiguous manner, utilizing different equation forms, boundary conditions, and ferromagnetic materials, all for educational purposes.

We present the study of environmental gradients such as altitudinal gradient, slope class, and aspect on the organic carbon stock of Wacho forest soil in south western Ethiopia. A systematic random sampling technique was used to collect the soil samples. The soil organic carbon stock was determined by a standardized mathematical equation. A one-way analysis of variance was used to test the effect of environmental gradients such as altitudinal gradient, slope class, and aspect on organic carbon stock of Wacho forest soil. Descriptive statistics were used to calculate the mean and standard deviation of the organic carbon stock of Wacho forest soil. The organic carbon stock of Wacho forest soil varied from 94.58 ± 9.6 t/ha (15.1–20% slope class) to 130 ± 14 t/ha (5–10% slope class). The organic carbon stock of Wacho forest soil ranged from 92 to 140 t/ha in the west and east, respectively. Both slope class and aspect had a statistically significant effect on organic carbon stock of Wacho forest soil.

A collocation method with an approximate function consisting of a combination of cubic B-spline functions was established to solve the regularized long wave (RLW) equation. To increase accuracy of the method, multi-step predictor–corrector time integrator is introduced to discretize the RLW equation. The space decomposition of the dependent variable and its derivatives of the RLW equation was accomplished via the B-spline collocation method. Open form of Adams-Bashforth-Moulton method is used as a predictor, then closed Adams-Bashforth-Moulton method is implemented as a corrector. Collocation predictor–corrector method provides an increase in accuracy. Comparison is made with results of some former studies. When high accuracy time discretization is used in getting the solution of the RLW equation, it is observed that the errors are more accurate than the results of the Crank-Nicolson finite element methods listed in the article.

The emission of polycyclic aromatic hydrocarbons (PAHs) due to coal co-combustion with corncob (0, 10, 20, and 30%) was studied through a pilot scale drop tube furnace. Total PAHs (∑PAH) emission (gas + particulate) increased linearly from 19.4 µg/m³ for coal combustion to 31.6, 39.8, and 42.0 µg/m³ for 10, 20, and 30% corncob blends, respectively. Low-molecular-weight PAHs dominated the gas phase; medium- and high-molecular-weight PAHs in the particle phase. Naphthalene is the most prominent PAH in the gas phase. Emission of benzo[a]pyrene, increased by 45.9% at 10% corncob blend. However, its emission decreased by  − 19.1% and  − 87.3% for 20 and 30% corncob blends. Toxicity equivalence was also relatively higher for the 10% corncob blend but decreased greatly at 20 and 30% blends. For coal combustion, PAHs are generated due to the pyrolysis process, whereas for coal-corncob co-combustion, pyro-synthesis is the major route of PAH formation, as the PAH content was maximum at the later stage of combustion, i.e., at the bottom zone of the furnace. This study indicated that a minimum of 20% blending of corncob is required to achieve the beneficial effect of coal co-combustion in decreasing the emission of toxic PAHs.