Search results

Let b¯2,3(n), which enumerates the number of (2, 3)-regular overcubic bipartition of n. The purpose of the paper is to describe some congruences modulo 8 for b¯2,3(n). For example, for each α ≥ 0 and n ≥ 1, b¯2,3(8n+5)≡0(mod8), b¯2,3(2⋅3α+3n+4⋅3α+2)≡0(mod8).

H.C. Chan has studied the congruence properties of cubic partition function a(n), which is defined by ∑n=0∞a(n)qn=1(q;q)∞(q2;q2)∞.

To establish several congruence modulo 8 for b¯2,3(n), here the author keeps to the classical spirit of q-series techniques in the proofs.

The results established in the work are extension to those proved in ℓ-regular cubic partition pairs.

This paper aims to analyze the pressure distribution of rectangular aerostatic thrust bearing with a single air supply inlet using the complex potential theory and conformal mapping.

The Möbius transform is used to map the interior of a rectangle onto the interior of a unit circle, from which the pressure distribution and load carrying capacity are obtained. The calculation results are verified by finite difference method.

The constructed Möbius formula is very effective for the performance characteristics researches for the rectangular thrust bearing with a single air supply inlet. In addition, it is also noted that to obtain the optimized load carrying capacity, the square thrust bearing can be adopted.

The Möbius transform is found suitable to describe the pressure distribution of the rectangular thrust bearing with a single air supply inlet.

The purpose of the study is to obtain and analyze vibro-acoustic characteristics.

A unified analysis model for the rotary composite laminated plate and conical–cylindrical double cavities coupled system is established. The related parameters of the unified model are determined by isoparametric transformation. The modified Fourier series are applied to construct the admissible displacement function and the sound pressure tolerance function of the coupled systems. The energy functional of the structure domain and acoustic field domain is established, respectively, and the structure–acoustic coupling potential energy is introduced to obtain the energy functional. Rayleigh–Ritz method was used to solve the energy functional.

The displacement and sound pressure response of the coupled systems are acquired by introducing the internal point sound source excitation, and the influence of relevant parameters of the coupled systems is researched. Through research, it is found that the impedance wall can reduce the amplitude of the sound pressure response and suppress the resonance of the coupled systems. Besides, the composite laminated plate has a good noise reduction effect.

This study can provide the theoretical guidance for vibration and noise reduction.

The purpose of this article is based on the unit patent license fee model in the closed-loop supply chain.

This paper analyzes the impact of the bundling strategy of the retailer selling new products and remanufactured products on the closed-loop supply chain under the condition that the original manufacturer produces new products and the remanufacturer produces remanufacturing products.

The results show that alternative products can be bundled, and in many cases, the bundling of remanufactured products and new products is better than selling alone.

If the retailer chooses bundling, for the remanufacturer, when certain conditions are met, the benefits of bundling are greater than the separate sales at that time; for the original manufacturer, when the recycling price sensitivity coefficient is high, the bundling is better than separate sales.

The author studies forms over finite fields obtained as the determinant of Hermitian matrices and use these determinatal forms to define and study the base polynomial of a square matrix over a finite field.

The authors give full proofs for the new results, quoting previous works by other authors in the proofs. In the introduction, the authors quoted related references.

The authors get a few theorems, mainly describing some monic polynomial arising as a base polynomial of a square matrix.

As far as the author knows, all the results are new, and the approach is also new.

The importance of sovereign bond as a source of financing revenue deficit, benchmarking for corporate bonds and debt management in Africa, calls for continual monitoring of its volatility dynamics. This study evaluates the nature of sovereign bond volatility interaction between African countries using bivariate BEKK-GARCH (1, 1) model. Based on a sample of eight African countries, the results show evidence of unidirectional volatility spillover from Morocco sovereign bond to Egypt sovereign bond. Next, the results show absence of volatility interaction between Ghana and Nigeria sovereign bonds. The results further show the existence of bidirectional volatility transmission between Uganda and Kenya. Finally, the results indicate evidence of bidirectional volatility interaction between Botswana and South Africa. Overall, the results show existence of full interaction between Uganda–Kenya and Botswana–South Africa sovereign bond returns, partial interaction between Egypt and Morocco sovereign bond returns and no interaction between Ghana and Nigeria sovereign bonds markets. Thus, these results provide valuable implications for sovereign and corporate credit risk management, as well as strategy for monitoring and minimising negative effect of sovereign bond volatility spillover in Africa.