Square Of Number Research Articles

On Strongest Algebraic Program Invariants

A polynomial program is one in which all assignments are given by polynomial expressions and in which all branching is nondeterministic (as opposed to conditional). Given such a program, an algebraic invariant is one that is defined by polynomial equations over the program variables at each program location. Müller-Olm and Seidl have posed the question of whether one can compute the strongest algebraic invariant of a given polynomial program. In this article, we show that, while strongest algebraic invariants are not computable in general, they can be computed in the special case of affine programs, that is, programs with exclusively linear assignments. For the latter result, our main tool is an algebraic result of independent interest: Given a finite set of rational square matrices of the same dimension, we show how to compute the Zariski closure of the semigroup that they generate.

Cry toxin expression in different plant parts of Bt cotton at different phenological stages

BackgroundCompared to Bollgard-I, the utilization of Cry2Ab protein in Bollgard-II cotton cultivars enhances insect control. Field and laboratory studies demonstrated reduction in the numbers of bollworm-infested terminals, squares, and bolls in Bollgard-II cotton lines when compared to both Bollgard-I and non-Bollgard cotton cultivars. This indicates that the combination of Cry2Ab with Cry1Ac increased the overall expression of proteins. The expression of Cry protein varied across different plant parts, such as leaves, bracts, squares, and bolls. As the season progresses, the expression of Cry protein decreased in these plant parts. Leaves exhibited the highest levels of Cry protein expression, followed by squares, flowers, and bolls. Variation in the expression levels of delta endotoxins in different plant parts was one of the contributing factors to the survival of pest populations on Bt cotton.ResultsUsing a commercially available QL 96 ELISA plate kit, the concentration of delta endotoxin in various plant parts at different phenological stages was determined in twelve BG-II cotton hybrids, namely Ajeet-155, JKCH-2245, RCH-3863, NCS-866, MRC-7373, JKCH-99, MRC-7387, NCEH-21, ANKR-3324, NCSI-1904, and NCHB 9902. Cry1Ac and Cry2Ab protein levels were determined from samples of flowers and fruiting parts (Rind, locule, seed, locule wall and seed) at 40, 75, 100 and 125 days after sowing (DAS) over two consecutive years 2018–2019 and 2019–2020. Cry1Ac protein content and expression was the highest at 100DAS in locule, seed and rind; followed by rind and locule wall and seed in green bolls at 125 DAS; followed by seed, locule, rind and flowers at 75 DAS; followed by flowers at 40 DAS in all the tested twelve Bollgard-II hybrids. Cry2Ab protein content and expression was the highest at 125DAS in locule wall and seed and rind, followed by seed, locule and rind in green bolls at 100 DAS, followed by seed, locule, rind and flowers at 75 DAS, then by flowers at 40 DAS in all the tested twelve Bollgard-II hybrids. Cry1Ac protein expression was less in comparison with Cry2Ab.ConclusionsThe research findings indicate that the locule of BG-II cotton plants exhibited the highest expression levels of Cry1Ac and Cry2Ab proteins, followed by the seeds, rind, locule wall, and flowers. These results provide valuable insights into the distribution of Cry protein expression in different plant parts, which can contribute to a better understanding of insect control in Bt cotton cultivars.

Vinpocetine improves dyskinesia in Parkinson's disease rats by reducing oxidative stress and activating the Wnt/β-catenin signaling pathway.

Parkinson's disease (PD) is the commonest neurodegenerative disorder. It reduces motor and cognitive function in patients. Vinpocetine (Vinp) has the effects of anti-inflammatory and antioxidant, and could improve cognitive function in patients. This study was aimed to investigating the therapeutic effects of Vinp on dyskinesia in a 6-Hydroxydopamine hydrobromide (6-OHDA)-induced PD rat model. We constructed a PD rat model by injecting 6-OHDA, and intervened with Vinp for 7 days. The motor function of the rats was evaluated by an open-field test and rotation test. Besides, H&E staining was applied to observe the changes of dopaminergic neurons in the striatum. The levels of superoxide dismutase (SOD) and malondialdehyde (MDA) in the rat striatum were detected. We assessed the impact of Vinp on α-synuclein (α-Syn) and Wnt/β-catenin signaling pathway-related molecules by western blot and qRT-PCR. Rats in the PD group showed reduced horizontal movement frequency and number of squares crossed, increased contact time and rotation frequency, and reduced number of dopaminergic neurons accompanied by severe morphological damage. Vinp treatment increased the horizontal movement frequency and number of squares crossed, reduced the contact time, and rotation frequency in PD rats. Also, Vinp downregulated α-Syn protein expression and MDA level, while upregulated SOD activity in the striatum of PD rats. Furthermore, Vinp treatment activated the Wnt/β-catenin signaling pathway in the striatum of PD rats. In conclusion, Vinp improved the dyskinesia in 6-OHDA-induced PD rats by alleviating oxidative stress, and these effects may be associated with activating the Wnt/β-catenin signaling pathway.

Comparing the influence of natural farming on cotton (Gossypium hirsutum) yield and economics with integrated and organic farming

Cotton, a vital global cash crop, influences the economy and sustainability. Natural farming is a cost-effective, eco-friendly method. This study examines Natural Farming's effects on cotton yield and the economics of cotton compared to Integrated and organic farming. Field experiments were conducted during 2021-22 and 2022-23 at Tamil Nadu Agricultural College, Coimbatore. The experiment consisted of eight treatments, laid out in Randomized Block Design and replicated thrice. The treatments consist of control (T1), various Indian Natural farming practices including Beejamirit as a seed treatment, Ghanajeevamirit as basal, Jeevamirit with irrigation water, crop residue mulch, intercroping with pulses (T2 to T5), Organic farming practices (T6), Integrated crop management (ICM) practices with organic pest control (T7) and ICM with chemical pest (T8). The results indicated a significant increase in yield components: sympodial branches plant-1 (12.85 and 13.40), number of squares (29.28 and 31.28), bolls plant-1 (10.74 and 11.32), and boll weight (4.30 and 4.38 g) under Integrated Crop Management practices in 2021-22 and 2022-23, respectively. However, organic farming practices, followed by natural farming practices, were at par with integrated crop management. Integrated crop management practices resulted in significantly higher seed cotton yields (2178 and 2232 kg/ha in 2021-22 and 2022-23, respectively) than organic and natural farming practices with a higher cost of cultivation and a gross return. Complete natural farming outperformed organic and integrated farming in cotton, yielding higher net returns and B: C ratios. This approach holds promise for enhancing yield, economic viability and environmental sustainability in cotton cultivation.

The square density of words having a sequence of FS-double squares

A square is a word of the form uu, where u is a non-empty word. The square density of a word is the ratio of the number of distinct squares in a word to its length. It is known that in a word w=a1a2…an, at most two different rightmost squares can start from a letter ai. A factor of w that begins with two rightmost squares in w is said to be an FS-double square. We identify the structure of words having k consecutive FS-double squares in which at least k locations start with no rightmost squares. We show that the square density of such words is less than 13381. We select the structure of FS-double squares that minimizes the number of locations starting with no rightmost squares and use it to obtain a new family of words. Every word of the family has consecutive FS-double squares. We then prove that the square density of these words increases with the size of the words and converges to one.

Neurodegenrative changes in retina of rats with streptozotocin-induced diabetes under conditions of treatment with niacin-oxy-ethylidene-diphosphonate germanate (MIGU-4)

Background: Diabetes is accompanied by neurodegenerative changes in the retina. The determination of retinal function parameters under conditions of experimental diabetes may allow for the development of new approaches to pharmacological vision correction. Purpose: To assess changes in the metabolic (lipid peroxidation and antioxidant defence) and functional characteristics (electroretinography (ERG)) of the retina in the rat with streptozotocin (STZ)-induced diabetes, treated with niacin-oxy-ethylidene-diphosphonate germanate (MIGU-4) and a reference drug, diazepam. Material and Methods: Diabetes was induced intraperitoneally (i.p.) in Wistar male rats by streptozotocin (STZ 65 mg/kg). Four weeks thereafter, the rats received a two-week course of a daily dose of MIGU-4 (5.0 mg/kg or 25.0 mg/kg) or diazepam (0.5 mg/kg or 1.5 mg/kg). The electroretinogram (ERG) was obtained, the animals were euthanized and retinal malondialdehyde (MDA) levels and superoxide dismutase (SOD) and catalase (CAT) activity were determined. Results: In rats with untreated STZ-induced diabetes, the retinal MDA level was 3.71 times increased and CAT activity was 35% lower, compared to controls, whereas the SOD activity was half of the activity found in controls (р less 0.05). In diabetic animals treated with MIGU-4 i.p. at a 25.0-mg/kg daily dose, the retinal MDA level was 63.2% lower, whereas the CAT activity and SOD activity were 41.9% and 27.6%, respectively, higher, than in untreated diabetic rats (р less 0.05). In diabetic animals treated with diazepam i.p. at a 1.5-mg/kg daily dose, the retinal MDA level was 59.2% lower, whereas the CAT activity and SOD activity were 44.4% and 32.1%, respectively, higher, than in untreated diabetic rats (р less 0.05). In untreated diabetic rats, the ERG b-wave amplitude was 39.2% lower, ERG a-wave and b-wave latencies, 23.4% and 14.0%, respectively, higher, and the a-wave amplitude recovery rate, 38.8% lower than in controls (р less 0.05). The use of a 25.0-mg/kg daily dose of MIGU-4 resulted in a 29.7% and 33.9%, respectively, increase in the ERG b-wave amplitude and the a-wave amplitude recovery rate compared to untreated diabetic rats (р less 0.05). The use of a 1.5-mg/kg daily dose of diazepam resulted in a 25.0% and 30.0%, respectively, increase in the above ERG parameters compared to untreated diabetic rats (р less 0.05). In untreated diabetic rats, the number of squares crossed (SK) was 29.4% lower (р less 0.05); the number of central squares crossed (CSC), 52.1% lower (р less 0.05); the number of upright postures (UP), 34.2% lower; and the defecation bolus number, 32.4% higher than in controls (р less 0.05). After MIGU-4 (25-mg/kg) withdrawal, there were no more differences in SK, CSC, UP and defecation bolus numbers between treated diabetic rats and controls. In addition, the number of CSC was 4.27 times lower than in controls, and half of that in untreated diabetic animals (р less 0.05). In diabetic rats treated with diazepam, the number of UP was 2.56 times lower than in controls (р less 0.05), and 40.7% lower than in untreated diabetic rats (р less 0.05), whereas the defecation bolus number was 40.5% higher than in controls (р less 0.05). Conclusion: STZ-induced diabetes is accompanied by an impairment of the oxidant/ antioxidant balance in the retina with an increase in retinal MDA, decrease in retinal SOD and CAT activity, and ERG abnormalities such as reduced ERG amplitude and increased ERG latency. A course treatment with niacin-oxy-ethylidene-diphosphonate germanate (MIGU-4) i.p. at a daily dose of 25.0 mg/kg provides for a decrease in retinal MDA and an increase in retinal SOD and CAT activity and ERG wave amplitude The withdrawal of a two-week treatment with MIGU-4 i.p. at a daily dose of 25.0 mg/kg decreased open-field anxiety-like behaviors, whereas the withdrawal of a two-week treatment with diazepam i.p. at a daily dose of 1.5 mg/kg increased open-field anxiety-like behaviors. The corrective effect of treatment with MIGU-4 corresponds to the corrective effect of treatment with diazepam.

A set of 2-recurrence whose perfect squares do not form a set of measurable recurrence

AbstractWe say that $S\subseteq \mathbb Z$ is a set of k-recurrence if for every measure-preserving transformation T of a probability measure space $(X,\mu )$ and every $A\subseteq X$ with $\mu (A)>0$ , there is an $n\in S$ such that $\mu (A\cap T^{-n} A\cap T^{-2n}\cap \cdots \cap T^{-kn}A)>0$ . A set of $1$ -recurrence is called a set of measurable recurrence. Answering a question of Frantzikinakis, Lesigne, and Wierdl [Sets of k-recurrence but not (k+1)-recurrence. Ann. Inst. Fourier (Grenoble)56(4) (2006), 839–849], we construct a set of $2$ -recurrence S with the property that $\{n^2:n\in S\}$ is not a set of measurable recurrence.

Concept Formation Processes of Area and its Formula with GeoGebra: Case of Rectangle

This research aims to investigate the construction of the area of rectangle with GeoGebra and how students can formulate it. It focuses on describing the cognitive process involved in constructing this concept and how technology mediates such a process. The research was conducted in a classroom with 5th grade students in a secondary school and was designed qualitatively as a case study. A readiness test was prepared to determine the preliminary knowledge of the students about the concept of area. The teaching process was carried out with the activities based on GeoGebra. Considering the test results, researcher observations, and teacher views, five voluntary participants were selected, and we had three interviews with each of them. The obtained data from the teaching process and interviews were analyzed according to APOS theoretical framework. The results of the research demonstrate that one of the participants could not conceptualize the area as an object as the number of unit squares that cover the area without any space, while two of the participants could not conceptualize the formula of area of rectangle as an object. The students generally had difficulty in encapsulating the concept of the area and its formula. Area conservation and unit concept are important for conceptualizing the concept of area by realizing the covering feature of it, and understanding the dimension relationship is significantly effective in conceptualizing its formula.

Squares in recurrences using elliptic curves

Numerous papers have studied the problem of determining upper bounds for the number of integer points on elliptic curves of the form [Formula: see text], and quartic curves of the form [Formula: see text]. Bounds for the number of integer solutions to such quartic equations typically depend on both of the coefficients [Formula: see text]. The purpose of this paper is to examine more closely how the number of integer points on such quartic curves seems to depend almost entirely on the number of prime factors of [Formula: see text]. This is done by focusing in on the problem of bounding the number of squares in certain recurrence sequences. In particular, using some arithmetic on elliptic curves, it is proved that infinitely many such sequences can have four squares, but that a fifth square remains elusive after extensive computation, suggesting that an absolute bound for the number of squares is more than likely, and also suggesting that the above assertion regarding the dependence on the number of prime factors of [Formula: see text].

Synthesis, crystal structure, and intrinsic reactivity descriptors of coordination complexes of [(cis-PdCl2·L-proline) L-proline] and [trans-PdCl2·(glycine-OMe)2

This work describes the synthesis and structural characterization of two palladium (II) complexes elucidated by infrared spectroscopy, dispersive energy analysis (EDS) with Scanning Electron Microscopy (SEM) and X-ray single-crystal diffraction analysis. The first chiral complex is derivatized from l-proline amino acid, obtaining [Cis-PdCl2·L-proline(L-proline)] (1), in which the structure does not have symmetry elements and crystallized in a triclinic crystal system on a non-centrosymmetric space group P1. The comparison with the structural complex of [trans-PdCl2·(glycine-OMe)2] (3) becomes necessary due to the anticancer activity of its analog, cis-platinum, and the catalytic activity caused by Pd as a metallic center. Complex 1 is therefore made up of a free proline molecule linked by a single hydrogen bond to a PdCl2 molecule forming a 5-member chelate ring of the COO···Pd···NH type with another proline molecule and displaying distorted angles and bond sizes to the square planar geometry of the palladium (Pd) center. Ring formation generates a new stereogenic center chemically correlated with the induction caused by the absolute configuration S of the initial amino acid. The crystal results strongly indicate the confirmed configuration by the Flack parameter and its crystal packing stabilization by an intermolecular H-bond network, highlighting as a secondary mimicking structure the β sheets formed by hydrogen bonding interaction of the N—H···Cl type responsible for the disorder moldered on pyrrolidine ring.Furthermore, the Pd(II) complex obtained by the glycine was [trans-PdCl2·(glycine-OMe)2] (3). Regarding its chemical structure, this complex is constituted by the union of two glycine methyl ester molecules binding to a Pd in a trans disposition concerning the almost perfect square plane, which also contains a C2 axis of rotation. Complex 3 crystallized in a monoclinic system and centrosymmetric space group P21/c, the packing is favored by four strong hydrogen bond type interactions presenting helices with 90° rotations between each layer.Owing to their great interest and relevance in Pd—N amino acid in catalytic and medicinal chemistry, the electronic and global reactivity properties of complexes 1 and 3 were further explored by computational methods in the framework of Density Functional Theory, finding 1 as the most reactive complex due to the narrower E-LUMO/E-HOMO energy gap, having this band gap in agreement with the lowest hardness value compared to those shown for 3, in which band gap and hardness are higher with a tendency to kinetic stability and controlled reactivity.

Coherences in the Dynamics of Physical Systems from a Multifractal Perspective of Motion.

Using an analogy between the multi-fractal Schrödinger equation and the dumped oscillator equation through a special ansatz, Stoler-type coherences in the dynamics of physical systems are highlighted. Such a result implies a Ricatti-type gauge, a process that can be considered a calibration of the difference between the kinetic and potential energy of a Lagrangian, specified as a perfect square in generic coordinates.

Response of Various Intercrops on Growth and Yield Attributes of Cotton (Gossypium hirsutum L.) under Irrigated Situation

Intercropping in cotton is one of the best approachs to improve the food security and soil fertility in addition to that of generating cash income of the rural poor. At present intercropping is common in conventional agriculture to augment the land use and also symbolic in reducing the weeds infestation. But, introducing superfluity population of intercrops without reducing the base crop population is of preeminence. Therefore field experiments were conducted at farmer’s field located at Erode District in Tamil Nadu, India (during 2018-2019) to investigate the compatible, remunerative and best smothering intercrops on the base crop, cotton. The experiment was outlayed in randomized block design with three replications. The treatment encompass of seven treatments viz., Cotton alone (Gossypium hirsutum L.), Cotton + Blackgram (Vigna mungo), Cotton + Greengram (Vigna radiata), Cotton + Cowpea (Vigna unguiculata), Cotton + Coriander (Coriandrum sativum), Cotton + Onion (Allium cepa) and Cotton + Sesame (Sesamum indicum). The study clearly showed that among the treatments Cotton + Cowpea showed superior response in growth attributes like plant height (harvest stage) (153.23 cm), LAI -Leaf Area Index at 70 DAS (6.18), DMP – Dry Matter Production at harvest ( 6788.01 kg per ha) and yield attributes like number of Monopodial branches per plant (3.22), number of Sympodial branches per plant (19.62), number of squares per plant (48.83), number of bolls per plant (32.23), boll weight (3.98 g) and seed cotton yield (2455.70 t ha-1) and next in order was Cotton + Blackgram. The result evidently proved that Cotton + Cowpea will be an appropriate intercropping system for cotton and it was having considerable increase in growth and yield of cotton.

Effect of acupuncture-moxibustion stimulation of combined "Biao-Ben" acupoints on autonomic nervous activity and related factors in rats with irritable bowel syndrome diarrhea

To observe the effect of acupuncture and moxibustion of the combined "Biao-Ben" acupoints on autonomic nervous function and related factors in rats with irritable bowel syndrome diarrhea (IBS-D). Female SD rats were randomly divided into normal control, IBS-D model, "Biao-Ben" acupoint combination, and conventional acupoint combination groups, with 10 rats in each group. The IBS-D model was established by repeated chronic stress stimulation (water or food deprivation, painful tail pinching, exposure to a 43 ℃ environment, forced swimming in 4 ℃ water, day-night inversion and horizontal vibration) for 28 d, and followed by acute restraint stress (wrapping of shoulders, forelimbs and trunk) for 1 h and gavage of senna fluid, once daily for 28 d. For rats of the "Biao-Ben" acupoint combination group, acupuncture and moxibustion were applied to "Guanyuan" (CV4), bilateral "Zusanli" (ST36), and "Neiguan" (PC6), and for rats of the conventional acupoint combination group, acupuncture and moxibustion were applied to bilateral ST36, "Tianshu"(ST25), and "Shangjuxu"(ST37). Both acupuncture and suspension moxibustion treatment were conduced for 15 min, once daily for 21 days. The fecal water content was calculated, and the spontaneous activity behaviors (total distance of crossing and the number of squares crossed in 5 min) were evaluated by open-field tests. The abdominal withdrawal reflex (AWR) was detected. H.E. staining was used to observe the histopathological changes of colon tissue. The domains of heart rate variability (HRV) including low frequency (LF), high frequency (HF), and LF/HF were analyzed using an electrophysiological recorder. The contents of calcitonin gene-related peptide (CGRP) in serum and noradrenaline (NE) in plasma were detected using ELISA. The expression level and immunoactivity of 5-hydroxytryptamine (5-HT) in colon tissues were detected by Western blot and immunofluorescence histochemistry, separately. Compared with the normal group, the model group had a striking increase in fecal water content, AWR scores at 20, 40, 60, and 80 mm Hg, NE and CGRP contents, LF, LF/HF, and 5-HT protein expression and immunoactivity (P<0.01), and an obvious decrease in the total distance of crossing, the number of squares crossed, and HF of HRV (P<0.01). In comparison with the model group, the fecal water content, AWR scores at 20, 40, 60, and 80 mm Hg, NE and CGRP contents, LF, LF/HF, and 5-HT protein expression and immunoactivity were significantly decreased (P<0.01,P<0.05), while the total distance of cros-sing, number of squares crossed, HF of HRV were considerably increased (P<0.01, P<0.05) in both "Biao-Ben" acupoint combination and conventional acupoint combination groups. The effects of the "Biao-Ben" acupoint combination were apparently superior to those of conventional acupoint combination in down-regulating the fecal water content, AWR score at 20, 40, 60 and 80 mm Hg, NE and CGRP contents, LF, LF/HF, and 5-HT expression and immunoactivity, and in increasing the number of squares crossed, and HF of HRV (P<0.01, P<0.05). HE staining showed no pathological changes in colonic mucosa in all groups. Acupuncture and moxibustion stimulation of combined "Biao-Ben" acupoints can effectively improve the symptoms (spontaneous activities, visceral hypersensitivity) of IBS-D model rats, which may be related to its functions in regulating autonomic nervous activities, and down-regulating blood NE and CGRP contents and colonic 5-HT protein expression and immunoactivity, and the effects of "Biao-Ben" acupoint combination are superior to those of conventional acupoint combination.

Optimal interpolation with spatial rational Pythagorean hodograph curves

Using a residuum approach, we provide a complete description of the space of the rational spatial curves of given tangent directions. The rational Pythagorean hodograph curves are obtained as a special case when the norm of the direction field is a perfect square. The basis for the curve space is given explicitly. Consequently a number of interpolation problems (G1, C1, C2, C1/G2) in this space become linear, cusp avoidance can be encoded by linear inequalities, and optimization problems like minimal energy or optimal length are quadratic and can be solved efficiently via quadratic programming. We outline the interpolation/optimization strategy and demonstrate it on several examples.

FEATURES OF THE “HEAT ISLAND” FORMATION OVER THE CITY OF NOVOVOLYNSK AND WAYS OF OPTIMIZING MICROCLIMATE CHANGES

The article is devoted to the problem of the formation and development of the urban “heat island” in the city of Novovolynsk. Human economic activity, the presence of a significant number of motor vehicles, asphalt and concrete surfaces, etc. cause significant differences between the microclimate of the city and the suburban area. Numerous experimental studies and measurements show that the surface temperature in cities is higher than in rural areas by 1-5°C.&#x0D; Therefore, the purpose of this study was to study the conditions of formation, the consequences of the formation of an urban heat island in the city of Novovolynsk and the development of measures to optimize microclimatic changes in the city.&#x0D; First of all, we analyzed literary sources and modern scientific publications and studied the theoretical foundations of the study of urban heat islands and methods of their evaluation. The climatic features of the city of Novovolynsk were studied and a number of measurements of temperature and humidity were carried out in the center of the city of Novovolynsk and on the outskirts of the city in the village of Stara Lishnya. These studies were carried out in order to experimentally determine the temperature difference between the city and the suburbs, as well as to identify the degree of influence of various types of anthropogenic activity.&#x0D; In the autumn and winter of 2022, we carried out a number of instrumental measurements of temperature and humidity in the center of the city of Novovolynsk (control point #1) and on the outskirts of the city in the village of Stara Lishnya (control point #2). The study showed that the highest repeatability of air temperature differences (both positive and negative) falls in the range of 0.5-1.0°С (42.8%) and less often the differences reach above 1.0°С (23, 8%) and below 0.4 (33.4%). The highest repeatability of air temperature excesses in the city center compared to the surrounding area is in the range from 0.5 to 1.0°С – at 2 p.m. o’clock. Evidence of the presence of an urban heat island in the city of Novovolynsk is also an analysis of air humidity indicators at control points. In particular, as a result of observations, a stable exaggeration of the relative humidity index in rural areas over indicators in the city center was recorded. Analysis of the obtained indicators shows that the air temperature above the center of the city of Novovolynsk is higher by 0.1–1.6°C than on the outskirts in neighboring villages.&#x0D; Finally, we developed a number of recommendations for optimizing thermal anomalies in the city of Novovolynsk. At the moment, several methods have been developed to solve the problem of thermal anomaly within urban urban areas, which can be summarized in the following steps: the use of “white roofs”, “green roofs”, planting more trees in the city, increasing the number of different squares and parks in the city, reducing the number of harmful emissions, thermal insulation of premises and buildings, use of solar panels etc.&#x0D; Key words: heat island, microclimate of the city, thermal anomalies, thermal pollution, temperature indicators, “green roofs”, “white roofs”.

Improving the success rate of quantum algorithm attacking RSA encryption system

Shor’s factorization algorithm (SFA) aims at finding the non-trivial factor of a given composite number, but the algorithm does not always work. In some cases, it has to call back to the beginning of the algorithm to make recalculation. After the analysis of the principle of SFA and the characteristics of RSA public-key cryptography with a series of data calculations, it can be concluded that the random value selected by the algorithm is closely related to whether the obtained period is effective. Therefore, a new optimized scheme is proposed to tackle with this defect from two perspectives: (a) When the a value is a perfect square, the algorithm can be completed with an odd cycle r. (b) When the period r obtained by the randomly selected a value is a multiple of 3, the algorithm can be completed by modifying the decomposition method to relax the requirements for the period without affecting the complexity of the algorithm. Due to the limitations of hardware in applying the quantum algorithms, the classical algorithm is applied to simulate quantum algorithms to test the success rate of decomposition of some composite numbers. The result indicates the effectiveness of the improved algorithm, which significantly reduces the probability of repeated operations to save the quantum circuit resources.

Determination of the Predominant Orientation of Cracks in Ice Cover of the Laptev Sea from the Ice Drift Data

Received April 10, 2023; revised May 25, 2023; accepted June 27, 2023The paper shows that in order to solve the problem of predicting the predominant orientation of cracks in ice covering the Laptev Sea, when the satellite information is absent, the orientation of cracks in ice cover can be calculated using data on the ice drift in the Sea. We have selected 200 satellite images made in both visible and infrared spectral bands allowing to obtain actual data on ice cracks in the Laptev Sea for seasons 2016–2021, and then calculated the predominant orientation of them using data on the OSI SAF ice drift for the date of each image as well as for several previous days. Results obtained were compared with actual modal orientations of the cracks and with characteristics of the atmospheric pressure fields in these days. It was found that selecting of initial ice drift data should be done with regard for the intensity of air flows, the invariability or constancy of the direction of air flows over the sea aquatory during several days, and the presence of a cyclone centered over the sea area. An algorithm has been developed for automatic selection of a date when the ice drift can be most likely accompanied by formation of cracks on the day under consideration, and calculation of predominant orientation of cracks should be made exactly on that day. The selected data on ice drift serve as a basis for calculating. It was revealed also that with the difference in the types of intensity of air flows in the northern and southern parts of the Laptev Sea, the developed algorithm for determining the date of ice drift should be applied to each part of the sea separately. The number of squares of the Laptev Sea grid in which the calculated orientation of cracks corresponded to its actual meaning with an established permissible error of 30° has been determined. The ratio of this number to the total quantity of grid squares (skill score) was equal to 69% on the average. The skill score exceeded 70% in 46 percent of the cases. The skill score falls below 60% in only 16 percent of the cases, with minimum value of 50%.

On the \(D(4)\)-pairs \(\{a, ka\}\) with \(k\in \{2,3,6\}\)

Let \(a\) and \(b=ka\) be positive integers with \(k\in \{2, 3, 6\},\) such that \(ab+4\) is a perfect square. In this paper, we study the extensibility of the \(D(4)\)-pairs \(\{a, ka\}.\) More precisely, we prove that by considering families of positive integers \(c\) depending on \(a,\) if \(\{a, b, c, d\}\) is a set of positive integers which has the property that the product of any two of its elements increased by \(4\) is a perfect square, then \(d\) is given by d=a+b+c+1/2(abc±√((ab+4)(ac+4)(bc+4))). As a corollary, we prove that any \(D(4)\)-quadruple tht contains the pair \(\{a, ka\}\) is regular.

New Discoveries in Number Theory and its Practical Application

This article shows new properties of positive integers related to the sum of the deviations of the products of dividing the positive number by each of its factors, as well as the positive integer with only three divisors called the perfect square with a square root as a prime number, and the article also shows the building scheme a computer application to find the number of divisors of a number, and to classify the number into prime and composite.

Solar Far Infrared-Induced Growth of Plants is Due to NonThermal Effect of Infrared to Radio-Frequency Electromagnetic Energy: Verification by Quantum Chemistry Molecular Modeling (DFT/MM)

This article shows new properties of positive integers related to the sum of the deviations of the products of dividing the positive number by each of its factors, as well as the positive integer with only three divisors called the perfect square with a square root as a prime number, and the article also shows the building scheme a computer application to find the number of divisors of a number, and to classify the number into prime and composite.