Reversibility of Circular Linear Cellular Automata over Finite Fields: An Exact Enumeration via the Unit Group of the Cyclic Group Algebra

Lee; Olalekan

Journal of International Economics Research | 2026

Economic Effects of AI Adoption in the Corporate Sector

The rapid development of digital technologies and artificial intelligence has significantly transformed the modern corporate environment. Artificial intelligence is increasingly used by companies to automate business processes, improve decision-making, and enhance operational efficiency. Therefore, studying the economic effects of AI adoption in the corporate sector has become highly relevant, especially for countries undergoing digital transformation such as Uzbekistan. The aim of this article is to analyze the economic impact of artificial intelligence adoption in the corporate sector and evaluate its influence on corporate productivity, operational efficiency, and profitability. The research is based on a quantitative analytical approach, including statistical analysis, comparative analysis, and case study methods. The empirical analysis was conducted using a sample of 30 companies from sectors such as banking, telecommunications, manufacturing, and information technology. The results show that companies implementing AI technologies demonstrate higher labor productivity (95,200 USD revenue per employee) compared to companies without AI adoption (71,400 USD). In addition, AI-adopting firms show lower operational costs (38% vs. 46%) and higher profitability indicators (ROA 11.8% compared to 7.4%). The findings confirm that artificial intelligence contributes to improving corporate efficiency and competitiveness. The practical significance of the study lies in providing evidence that AI adoption can support the development of the digital economy and enhance corporate performance in Uzbekistan.

groups

Artur Aleksandrovich Kim mail

link https://doi.org/10.54216/JIER.030201

Volume & Issue

Vol. Volume 3 / Iss. Issue 2

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Journal of International Economics Research | 2026

Remote Employment and Macroeconomic Transformation in the Digital Economy

The rapid development of digital technologies has significantly transformed labor markets and created new forms of employment organization. One of the most important trends in the digital economy is the expansion of remote employment, which allows employees to perform professional tasks outside traditional workplaces. The relevance of this study is determined by the growing importance of remote work and its potential macroeconomic effects on labor markets, productivity, and economic development. The aim of this article is to analyze the macroeconomic implications of remote employment and evaluate its role in the transformation of the labor market in Kazakhstan. The research is based on a quantitative analytical approach, including statistical and comparative analysis of employment data. The empirical study covered 24 organizations across four economic sectors, including information technology, finance, education, and professional services. The results show that the share of remote employees varies between 27.8% and 48.5% depending on the sector, with the highest level observed in the information technology industry. At the national level, the number of remote workers in Kazakhstan reached approximately 46,700 employees, representing about 0.5% of the total employed population. The findings indicate that remote employment contributes to increased labor flexibility and productivity in digitally intensive sectors. The study highlights the importance of developing digital infrastructure and improving digital skills to support the expansion of remote employment and strengthen the digital economy.

groups

Galiya Rakhmetovna Dauliyeva mail

link https://doi.org/10.54216/JIER.030202

Volume & Issue

Vol. Volume 3 / Iss. Issue 2

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Journal of International Economics Research | 2026

Global Food Market Integration and its Implications for National Food Security

The stability of global food markets has become a critical factor influencing national food security in many countries. In recent years, global food systems have experienced significant volatility due to economic globalization, climate change, geopolitical conflicts, and disruptions in international supply chains. These factors have increased the vulnerability of national food systems, particularly in countries that depend heavily on imported agricultural products. Therefore, studying the relationship between global food markets and national food security is highly relevant for ensuring sustainable economic and social development. The aim of this article is to analyze the impact of global food market dynamics on national food security and to evaluate the relationship between international food trade, food price volatility, and national food supply stability. The research is based on a quantitative analytical approach, including statistical analysis and comparative analysis of international food security indicators. The empirical analysis covers a sample of 20 countries, including 12 food-import-dependent countries and 8 agricultural exporting countries. The results show that the average Food Import Dependency Ratio reached 54.2% in import-dependent countries, while the average Global Food Security Index score was 62.4 compared with 71.8 in exporting countries. The study also identified significant volatility in the FAO Food Price Index, which increased from 98.1 in 2020 to 143.7 in 2022. The findings confirm that strengthening domestic agricultural production while maintaining balanced participation in global food markets can significantly improve national food security and enhance the resilience of food systems.

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Marina Rudolfovna Li mail -

Sergey Alekseevich Shoba mail

link https://doi.org/10.54216/JIER.030203

Volume & Issue

Vol. Volume 3 / Iss. Issue 2

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Journal of Sustainable Development and Green Technology | 2026

Increasing Bank Revenues through Open Banking and API-Based Services: Prospects for Uzbekistan

Presently, there has been increasing policy attention from financial regulators in emerging banking systems on the need to look into the institutional mechanisms that could strengthen revenue generation of commercial banks in digital banking ecosystems. This study was an attempt to highlight the role of Open Banking platforms and API-based financial services in determining bank revenue growth in digital banking markets & financial service ecosystems (Uzbekistan). Therefore, the empirical findings of the present study can be used to better comprehend how Open Banking frameworks could be implemented in enhancing bank revenue streams in Uzbekistan. The previously developed Open Banking adoption indicators, API service readiness indicators, and bank revenue determinants framework in digital financial studies were used to collect data from banking professionals in commercial banks and fintech institutions. AHP’s prioritization results and structural equation modeling results on Open Banking adoption and API service integration increased significantly after evaluation with the support of the SEM analytical model. Additionally, the results of AHP analysis showed that Open Banking services and API-enabled platforms were the main areas of priority to be adopted by commercial banks on the basis of revenue-generation potential and service-integration capability, respectively. Moreover, the results also showed that out of five determinants, API service integration played a significant role in linkages between Open Banking adoption and bank revenue growth. The implications derived from this study can be used for enhancing bank revenue diversification in the context of Open Banking ecosystems. The finding is important given that higher levels of the Open Banking infrastructure are often found in digital banking systems of developed economies which cost less per unit of financial transaction – as there is less manual processing involved.

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Gulchekhrakhon Ostonakulova mail

link https://doi.org/10.54216/JSDGT.060101

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Pure Mathematics for Theoretical Computer Science | 2026

An Introduction to Probability, Hyper-Probability, and Super-Hyper-Probability

Standard probability theory assigns each event a single real value in [0, 1], satisfying non-negativity, normalization, and countable additivity. Hyper-Probability extends this notion by assigning to each event a set of probability values in [0, 1], thereby capturing multiple independent assessments from diverse sources. Super-HyperProbability further generalizes the framework by mapping events to iterated power sets of [0, 1], modeling hierarchical uncertainty across multiple aggregation levels. In this paper, we formally define the Hyper-Probability Measure and Hyper-Probability Distribution, examine their fundamental properties, and demonstrate how these constructs unify and extend classical probability within the Hyper- and Super-HyperProbability paradigms.

groups

Takaaki Fujita mail -

Ajoy Kanti Das mail

link https://doi.org/10.54216/PMTCS.060101

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Pure Mathematics for Theoretical Computer Science | 2026

HybridFunctorial Structure and MultiFunctorial Structure

A Functorial Structure is defined as a covariant functor F : C → Set, assigning sets to objects and functions to morphisms, ensuring functoriality. In this paper, we introduce and formally define two new concepts: the HybridFunctorial Structure and the MultiFunctorial Structure. A HybridFunctorial Structure combines two functors on the same category, linked by a natural transformation, ensuring consistent pushforward compatibility. A MultiFunctorial Structure involves multiple functors indexed by a preorder, coherently related via natural transformations, forming compatible families with functorial consistency.

groups

Takaaki Fujita mail -

Ajoy Kanti Das mail

link https://doi.org/10.54216/PMTCS.060102

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Pure Mathematics for Theoretical Computer Science | 2026

Spectral Moment Invariants and the Weisfeiler–Leman Hierarchy: Separating Power, a Fundamental Limitation, and Three Open Problems

We study spectral moment invariants Σp(G) = (trAG, . . . , trApG), built from the adjacency spectrum of a graph G, as graph isomorphism invariants positioned relative to the Weisfeiler–Leman (WL) hierarchy used to characterize graph neural network (GNN) expressivity. We give three fully verified case studies. First, C6 vs. 2K3: a 1- WL-indistinguishable pair separated by Σ3 but not Σ2 or Σ4. Second, K3,3 vs. the triangular prism: a second 1-WL-indistinguishable, cubic pair, also separated at order 3, but where the fourth moment separates as well, showing separating power is graph-family dependent even at fixed order. Both examples are grounded in a general fourth-moment identity (Proposition 2.8) and a homomorphism-counting identity (Proposition 2.5) that we prove from first principles. Third, and in the opposite direction, we prove that spectral moment invariants of every finite order fail on the classical cospectral, non-isomorphic strongly regular pair srg(16,6,2,2) (the Shrikhande graph and the 4×4 rook’s graph), verified numerically to fourth order by two independent methods. We situate both directions within published enumeration data and the Godsil–McKay switching construction, compare the computational complexity of spectral-moment, WL, and general isomorphism testing, connect the limitation to Laplacian eigenvector positional encodings in Graph Transformers, and pose three precise open problems.

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Murat Ozcek mail

link https://doi.org/10.54216/PMTCS.060103

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Pure Mathematics for Theoretical Computer Science | 2026

Interval-Lattice Fixed-Point Semantics for Certified Implicit Hypergraph Neural Operators

Implicit hypergraph models represent higher-order propagation by an equilibrium equation, but standard wellposedness arguments typically force a contraction and therefore exclude noncontractive yet order-preserving dynamics. This paper introduces an interval-lattice semantics for implicit hypergraph neural operators. On the box lattice L = {X ∈ Rn×d : ℓ ≤ Xi j ≤ u}, a normalized hypergraph propagation PH ≥ 0, an entrywise nonnegative channel map A ≥ 0, and an isotone activation generate an order-preserving operator T : L →L. The Knaster– Tarski theorem then yields a nonempty complete lattice of equilibria without requiring ∥A∥ < 1. Coupled iterations from the bottom and top elements produce certified lower and upper enclosures for every equilibrium. Under the optional metric condition q = Lσ ∥PH ∥2 ∥A∥2 < 1, the extremal equilibria coincide; geometric convergence, a residual-to-solution certificate, and a structural perturbation bound follow. Permutation equivariance and monotone dependence on input features are also proved. Two small arithmetic tables illustrate certificate scaling rather than empirical performance. The paper concludes with seven open problems on noncontractive uniqueness, signed hypergraphs, finite certificate complexity, topology-aware perturbation metrics, expressivity, differentiable extremal selection, and asynchronous lattice iteration.

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Sawsan Rateb almokabaa mail -

Maissam Ahamad Jdid mail

link https://doi.org/10.54216/PMTCS.060104

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

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Pure Mathematics for Theoretical Computer Science | 2026

Residuation–Galois Calculus for Exact Safety Preimages of Monotone Max–Plus Neural Networks

A proof-only calculus is developed for exact set abstraction and backward safety certification of monotone neural operators. A Galois insertion between concrete sets and interval boxes yields the best correct interval transformer. For every coordinatewise monotone map F, this transformer maps [ℓ,u] exactly to [F(ℓ),F(u)]; hence layerwise interval propagation is hull-exact for networks with nonnegative weights and isotone activations. The analysis is sharpened for max–plus layers T(x) =W ⊗x⊕b. Their upper safety preimages are either empty or principal ideals generated by the residualW\y, where (W\y)i = inf j:Wji>−∞(yj−Wji). Reverse residual propagation through a depth-L network computes the greatest input vector satisfying a prescribed upper output bound. Consequently, the largest weighted ℓ∞ radius around a nominal input is obtained in closed form, without optimization, branching, sampling, or relaxation. Soundness, maximality, compositionality, exactness, homogeneous collapse, and target-bound stability are proved. Four open problems concern signed architectures, two-sided class margins, residuated transformer attention, and completeness beyond boxes.

groups

Nader Taffach mail -

Mohammad Al-Shiekh mail

link https://doi.org/10.54216/PMTCS.060105

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

Details open_in_new

Pure Mathematics for Theoretical Computer Science | 2026

Reversibility of Circular Linear Cellular Automata over Finite Fields: An Exact Enumeration via the Unit Group of the Cyclic Group Algebra

We study the reversibility of one-dimensional linear cellular automata (CA) with periodic boundary conditions over a finite field Fq, identifying the global transition map with multiplication by a rule polynomial f (x) in the cyclic group algebra Rn = Fq[x]/(xn−1). We prove that reversibility is exactly equivalent to f (x) being a unit of Rn, and, when gcd(n,q) = 1, we use the classical correspondence between irreducible factors of xn−1 and q-cyclotomic cosets modulo n to derive a closed-form count of the reversible rules of a given neighborhood size: |R×n | = Πi(qdi −1), where the di are the sizes of the q-cyclotomic cosets modulo n. We then resolve the complementary case gcd(n,q)>1: writing n = pam with p = char(Fq) and gcd(m, p) = 1, we show xn−1 = (xm−1)pa , determine the local structure of each factor ring Fq[x]/(g(x)pa) for g irreducible, and obtain the fully general count |R×n| = Πi qdi(pa−1)(qdi −1), valid for every n and every finite field Fq. We give an explicit closed form for the case where m is prime and q is a primitive root modulo m, a density lower bound, an explicit description of the group of reversible rules under composition together with a formula for the exact dynamical period of any reversible rule via its coordinates under the Chinese Remainder Theorem, and a remark on explicit inverse-rule construction. All results are stated and proved in full; numerical instances used to validate the formulas were checked by direct and brute-force computation and are reported without tabulation.

groups

Lee Xu mail -

Olalekan Joosati mail

link

Volume & Issue

Vol. Volume 6 / Iss. Issue 1

Details open_in_new