We extend the theory of quasi-invariant states for compact group actions on C^* -algebras to the setting of semidirect product groups. Given a compact semidirect product K=G⋊ _ϕH , where ϕ is a continuous homomorphism from H into Aut(G) , we characterize actions of K on C^* -algebras in terms of compatible actions of the component groups G and H. We establish the fundamental properties of K-quasi-invariant states, including cocycle identities, lifting to von Neumann algebras, averaging properties, and prove the main result that under appropriate modular commutation conditions, the GNS representation of a quasi-invariant state is unitarily equivalent to that of its averaged state. This generalizes the framework established by Griseta [3] for single compact groups.
This article considers the linear Volterra-Stieltjes integral equation of the third kind. To solve this equation, a regularizing operator is constructed and a uniqueness theorem is proven. The research uses the concept of a derivative with respect to an increasing function, the method of regularization according to M. M. Lavrent'ev's methods in functional analysis, methods of transformation of equations, and methods of integral and differential equations. The proposed methods can be used to study integral and integro-differential equations of the Volterra-Stieltjes type of higher orders, as well as in the qualitative study of some applied processes in the fields of physics, ecology, medicine, and the theory of control of complex systems. They can be used in the further development of the theory of integral equations in classes of ill-posed problems, in the numerical solution of Volterra-Stieltjes integral equations of the third kind, and when solving specific applied problems that lead to equations of the third kind.
The Kyrgyz food industry relies on significant raw material potential. Improving public health through healthy food is one of the state’s priorities, especially due to the growing incidence of anemia and thyroid diseases associated with iron and iodine deficiencies. This article describes a novel yak meatloaf fortified with plant-based iodine. To evaluate its ability to address micronutrient deficiencies, the authors conducted a comprehensive assessment of its mineral composition, sensory properties, and microbiological safety. The experimental meatloaf consisted of shoulder-blade yak meat and dried kelp (imported from China). Its mineral composition was determined using inductively coupled plasma atomic emission spectroscopy. The microbiological parameters, toxicity levels (mercury, arsenic, lead, cadmium), and pesticide content were analyzed using standard methods. The optimal dose of the iodinecontaining supplement was determined via sensory assessment based on a nine-point scale. The iodine content in the yak meat and kelp was 3.82 μg/100 g and 516.0 μg/100 g, respectively. The optimal proportion of kelp was found to be 1.5% of the raw material weight. The iodine content in the finished product reached 20.9 μg/100 g, compared to 4.87 μg/100 g in the control sample without kelp. The iron content in the final meatloaf reached 5.03 mg/100 g, compared to 2.61 mg/100 g in the control sample. Despite heat-induced losses, the final meatloaf contained 20.9 μg/100 g of iodine and 5.03 mg/100 g of iron. This kelp-fortified meatloaf demonstrated reliable functional properties and can be recommended for therapeutic diets fortified with iodine and iron.
This research aimed to incorporate apple pomace into fruit bar formulations and analyzed quality properties (chemical, physical, color and sensory parameters and biological active ingredients) of the obtained bars. For this purpose, most preferred formulation has been developed using apple pomace, raisins, peanuts, corn semolina, and honey. Then, the chemical composition, the total phenolic content, the total flavonoid content, the antioxidant activity, and the physical properties of the bar were analyzed. According to the results the optimized bar contained 18.7% moisture, 1.8% ash, 9.8% protein, 10.1% lipid, 8.7% dietary fibre, 58.5% total carbohydrate, 1.1% acidity, pH 4.4 and 364 kcal/100g energy. Furthermore, the bar contained 2.386 mg GAE (Gallic Acid Equivalent) kg-1 db (dry basis) of total phenolics and 850 mg CE (Catechin Equivalent) kg-1 db of total flavonoids. The antioxidant activity of fruit bar using by DPPH (2.2-diphenyl-1-picrylhydrazyl radical-scavenging activity), FRAP (Ferric Reducing Antioxidant Power) and CUPRAC (Cupric Reducing Antioxidant Capacity) assays were determined as 25.372 mg TEAA (Triethylammonium Acetate) kg-1 db, 8.701 mg TEAA kg-1 db, and 5.134 mg TEAA kg-1 db, respectively. Also, physical characteristics such as a hardness (94.2±19.1), cohesiveness (0.50±0.12), springiness (0.27±0.09), chewiness (28.2±5.20) and elasticity (0.62±0.06) were determined. Color parameters L, a* and b* were evaluated for the fruit bar. Moreover, sensory analysis revealed that the developed bar had a high level of general appreciation. Effect of storage period on moisture, pH and hardness of fruit bar was also analyzed. Therefore, incorporation of apple pomace in the bar formulation was a good way to evaluate the apple juice waste and can be used in the production of value-added product.
This study aimed to examine the acute and chronic effects of a standard race load and an eight-week training period on heart rate and respiratory function parameters in short-, middle-, and long-distance runners. The study was designed as a quasi-experimental study with a repeated-measures design. The research group consisted of short-distance (n = 11), middle-distance (n = 13), and long-distance (n = 10) female runners who were actively engaged in athletics. Resting, post-race, and recovery heart rate values (1 and 15 min post-exercise) were measured. Respiratory function parameters (FVC, FEV1, and PEF) were assessed before and immediately after exercise. Measurements were conducted at baseline and repeated after an eight-week training period. A mixed-design repeated-measures ANOVA was used to examine the effects of group, time, and period on physiological variables. Resting heart rate values were similar in short- and middle-distance runners, whereas long-distance runners exhibited lower values. Heart rate responses during post-race and recovery periods differed across disciplines, with short-distance runners showing a faster decline in the early recovery phase and long-distance runners reaching lower levels during the later recovery stage. Regarding respiratory function, post-exercise increases in FVC were observed in short- and middle-distance runners during the second measurement period, while FEV1 remained unchanged. PEF values increased only in short-distance runners during the same period. The eight-week training period did not significantly affect heart rate, and a significant increase was observed in FVC, whereas FEV1 remained unchanged. Recovery patterns also differed between disciplines, with short-distance runners showing a faster decline in heart rate during the early recovery phase, whereas long distance runners reached lower heart rate values during the later stages of recovery. These findings indicate that the changes observed following an 8-week period differ across running disciplines and exhibit a discipline-specific pattern. Not applicable, as this study is not a clinical trial.
