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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.

Let p_[1,r;t] be defined by ∑n=0∞p[1,r;t](n)qn=(E1Er)t, where t is a non-zero rational number, r ≥ 1 is an integer and Er=∏n=0∞(1−qr(n+1)) for |q| < 1. The function p_[1,r;t](n) is the generalisation of the two-colour partition function p_[1,r;−1](n). In this paper, the authors prove some new congruences modulo odd prime ℓ by taking r = 5, 7, 11 and 13, and non-integral rational values of t.

Using q-series expansion/identities, the authors established general congruence modulo prime number for two-colour partition function.

In the paper, the authors study congruence properties of two-colour partition function for fractional values. The authors also give some particular cases as examples.

The partition functions for fractional value is studied in 2019 by Chan and Wang for Ramanujan's general partition function and then extended by Xia and Zhu in 2020. In 2021, Baruah and Das also proved some congruences related to fractional partition functions previously investigated by Chan and Wang. In this sequel, some congruences are proved for two-colour partitions in this paper. The results presented in the paper are original.

The 1997-98 financial crisis has had a profound effect on how East Asian economies the role of the IMF and its strategic interests relative to those of the United States in the international financial regime. It has prompted them to create a regional mechanism for financial and monetary cooperation, ranging from deeper policy dialogue and surveillance, to a system of financial cooperation, and common exchange rate arrangements. This paper analyses the economic and strategic motivations behind this and outlines recent developments in financial cooperation in East Asia to provide possible directions for the future.

A network of bilateral swap arrangements under the Chiang Mai Initiative(CMI) needs stronger policy dialogue and surveillance to develop into a regional financing facility, a sort of East Asian IMF. The facility plays a role as an regional lender of last resort, providing short-term funds to a member country facing a temporary liquidity shortage and for market intervention to stabilize foreign exchange rate. East Asian countries need to achieve regional exchange rate stability. In the long run, the region may develop a common currency arrangement, but it cannot be expected in the very near future because there is no convergence of macroeconomic conditions, economic structure and systems. A realistic approach would be for East Asian developing countries to adopt a currency basket system to minimize the impact of dollar/yen exchange rate volatility on their economies. Strong political will and a vision for regional integration will be required to introduce it.

Arrangements for regional economic integration, under the WTO system, have unexpectedly dominated globalization. In fact, countries that have realized economic arrangements, such as the EU 's monetary union, are further expanding their efforts to achieve political integration. Regional economic integration is now considered an exigency of national affairs. North East Asian countries are also affected by this global predicament, but the issue involves greater structural complexities in this region. The emergence of China has forced Japan and Korea to contemplate difficult structural adjustments. For example, while the Korean government recognizes the importance of stronger intra-regional economic cooperation, by pursuing these arrangements it simultaneously faces the dilemma of maintaining traditional partnerships, such as those with the USA and Japan. If Korea actively supports regional economic arrangements, this action would be perceived as a bias toward China, consequently damaging ties with the US. Thus, rather than depending on public initiatives to establish economic ties in North East Asia, China, Japan and Korea should rely on market friendly projects initiated by the private sector that endorse gradual integration through non-political activities and exchanges among the citizens of the respective countries. This paper first proposes the founding of a North East Asian United University Community composed of students, professors and campuses of the three countries in the initial stages. Secondly, it proposes the development of unique Asian commodities, a concept similar to that of 'Airbus. ' Finally, it proposes utilization of retired Japanese, Korean and Chinese engineers and technicians to speed up the overall level of technology, which is critical to overcoming backwardness in this region.

Let X⊂ℙr be an integral and non-degenerate complex variety. For any q∈ℙr let rX(q) be its X-rank and S(X,q) the set of all finite subsets of X such that |S|=rX(q) and q   ∈  〈S〉, where 〈〉 denotes the linear span. We consider the case |S(X,q)|>1 (i.e. when q is not X -identifiable) and study the set W(X)q:=∩ S∈S(X,q)〈S〉, which we call the non-uniqueness set of q. We study the case dimX=1 and the case X a Veronese embedding of ℙn. We conclude the paper with a few remarks concerning this problem over the reals.

The authors discover a new identity concerning differentiable mappings defined on m-invex set via fractional integrals. By using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized relative semi- m-(r;h1,h2)-preinvex mappings by involving generalized Mittag-Leffler function are presented. It is pointed out that some new special cases can be deduced from main results of the paper. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well.

This paper aims to develop a credit-risk model in which firms face rollover risk, and the markets for defaulted assets are segmented due to entry costs. The paper shows that reducing the entry costs in this economy may decrease the total surplus of the economy. This outcome can arise because when market barriers are lifted, the gap between the liquidation prices across the markets will shrink, but then the market that would experience a price drop may face more bankruptcies because the rollover risk will increase in that market. The paper describes under which condition such an intervention policy improves or hurts the total surplus.

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 objective of this study is to present a successful strategy to promote Korea as the logistics hub of Northeast Asia. Firstly, we introduce the necessity of a logistic hub strategy for Korea. In order to develop a successful strategy, we consider the 'free trade zone' model of the Netherlands and China. We develop a realistic and suitable model for Korea based on this Jree trade zone' model. Our proposal for a successful logistic hub strategy for Korea is the fulfillment of the following six objectives: 1) security of market accessibility, 2) improvement of the logistic system, 3) improvement of the education system, 4) improvement of the tax system, 5) assurance of labor market flexibility, and 6) development of an appealing living environment for foreigners.

The purpose of this paper is to examine the effectiveness of an improved dummy variables control grey model (DVCGM) considering the hysteresis effect of government policies in China's energy intensity (EI) forecasting.

Energy consumption is considered as an important driver of economic development. China has introduced policies those aim at the optimization of energy structure and EI. In this study, EI is forecasted by an improved DVCGM, considering the hysteresis effect of energy-saving policies of the government. A nonlinear optimization method based on particle swarm optimization (PSO) algorithm is constructed to calculate the hysteresis parameter. A one-step rolling mechanism is applied to provide input data of the prediction model. Grey model (GM) (1, N), DVCGM (1, N) and ARIMA model are applied to test the accuracy of the improved DVCGM (1, N) model prediction.

The results show that the improved DVCGM provides reliable results and works well in simulation and predictions using multivariable data in small sample size and time-lag virtual variable. Accordingly, the improved DVCGM notes the hysteresis effect of government policies and significantly improves the prediction accuracy of China's EI than the other three models.

This study estimates the EI considering the hysteresis effect of energy-saving policies in China by using an improved DVCGM. The main contribution of this paper is to propose a model to estimate EI, considering the hysteresis effect of energy-saving policies and improve forecasting accuracy.