L. N. Gumilyov Eurasian National University

In the present study, we explore the cosmological implications of Rényi holographic dark energy within the framework of f(R,T) gravity by considering an anisotropic Kantowski–Sachs space time. To obtain exact solutions, we employ Berman’s law corresponding to a constant deceleration parameter and assume a proportional relationship between the shear scalar and the expansion scalar. The derived model exhibits a gradual decrease in the RHDE density as the Universe evolves, eventually tending toward a finite positive value at late times. At the same time, the pressure remains negative throughout the evolution and approaches a nearly constant value in the asymptotic regime. The behaviour of the equation of state parameter indicates a transition from values near zero to more negative values, supporting the onset of accelerated expansion. Our analysis shows that the Null Energy Condition (NEC) and the Dominant Energy Condition (DEC) remain satisfied; however, the Strong Energy Condition (SEC) is violated, consistent with late-time acceleration. Statefinder diagnostics reveal that the model evolves toward the ΛCDM fixed point. Although the squared sound speed is negative, reflecting non-canonical perturbative behaviour common in modified gravity, the background evolution remains well behaved. Overall, RHDE in f(R,T) gravity provides a viable description of late-time cosmic acceleration.

A class of viable F(R) gravity models which can provide a unified description of inflation with the dark energy era is confronted with the latest observational data on the dark energy era. These models have the unique characteristic that the de Sitter scalaron mass in the Einstein frame counterpart theory is a monotonic function of the curvature, which renders them viable descriptions for both the inflationary and the late-time acceleration eras. We also compare these models with other wellknown viable F(R) gravity models and with the Lambda-Cold-Dark-Matter model. As we show, the most phenomenologically successful models are those which deviate significantly from the Lambda-Cold-Dark-Matter model. Also some of the models presented, provide a statistically favorable description of the dark energy eras, compared with the exponential F(R) gravity model and of course compared with the Lambda-Cold-Dark-Matter model. All the models we present in this article are confronted with the observational data from the Planck collaboration, the Pantheon plus data from Type Ia supernovae, the two rounds of observations of the Dark Energy Spectroscopic Instrument, data from baryon acoustic oscillations and the Hubble constant measurements. As we show, two of the models are statistically favorable by the data.

We present a comprehensive analysis of inflationary models in light of projected sensitivities from forthcoming CMB and gravitational wave experiments, incorporating data from recent ACT DR6, DESI DR2, CMB-S4, LiteBIRD, and SPHEREx. Focusing on precise predictions in the (ns, as, fis) parameter space, we evaluate a broad class of inflationary scenarios-including canonical single-field models, non-minimally coupled theories, and string-inspired constructions such as Starobinsky, Higgs, Hilltop, a-attractors, and D-brane models. Our results show that next-generation observations will sharply constrain the scale dependence of the scalar power spectrum, elevating as and fisas key discriminants between large-field and small-field dynamics. Strikingly, several widely studied models-such as quartic Hilltop inflation and specific DBI variants-are forecast to be excluded at high significance. We further demonstrate that the combined measurement of fis and the field excursion Delta cent offers a novel diagnostic of kinetic structure and UV sensitivity. These findings underscore the power of upcoming precision cosmology to probe the microphysical origin of inflation and decisively test broad classes of theoretical models.

The article is relevant because of the need to formulate and consider the main tools of digital socioeconomic transformation, as well as because of the need to create a new model. The implementation of the transformation of already existing forms and concepts inherent in socioeconomic systems depends on these processes. It is shown that whereas in traditional industries, economic value is created within the enterprise, in the digital economy, value is created outside the enterprise at the time of interaction between partners, suppliers, and customers. The conceptualization of space activities in the Republic of Kazakhstan and the practical implementation of programs for the development of the space industry is considered. Based on a combination of process, sectoral, and technological approaches, the article considers the relationship between the development directions of the space industry in Kazakhstan and the processes of the national economy digitalization. The necessity of transnational strategic partnership in the field of innovative digital technologies in the space industry instead of the currently used "rent" approach is demonstrated. The results of the article can be used to develop White papers and more detailed documents in the field of interrelated policies for the development of the digital economy and the space industry in Kazakhstan.

Vegetable spoilage is a major contributor to global food loss, with potatoes being especially vulnerable due to their high nutrient content and microbial susceptibility. This study introduces a real-time, non-invasive method for detecting potato spoilage using a metal oxide semiconductor (MOS) gas sensor array, focusing on the MQ-3 sensor. An Arduino-based system continuously monitored gas emissions under ambient, high-humidity, and UV-treated storage conditions. Sensor data were validated against microbiological analysis, including E. coli, coliforms, total aerobic counts, yeast, and mold. A strong correlation was observed between sensor resistance decline and microbial growth, with MQ-3 showing high sensitivity to volatile organic compounds (VOCs). UV pretreatment delayed microbial activity and stabilized sensor signals. Comparative analysis revealed that only MQ-3 and MQ-135 were effective for early potato spoilage detection. These findings demonstrate the potential of low-cost MOS sensors as practical alternatives to traditional methods, enhancing food safety and reducing post-harvest losses.