Using multi-frequency electrical conductivity measurement to determine the selective salinity in a two-component salt solution

Received: January 12th, 2023 ; Accepted: April 27th, 2023 ; Published: July 19th, 2023 ; Correspondence: [email protected] technologies can help farmers produce safe, sustainable, high-quality food while contributing to the fight against effects of abiotic and edaphic factors. Due to digitalization, a paradigm shift occurred in agriculture, which boosted sensor technology's rapid development, especially soil sensors. Using sensors and the digital knowledge of soil properties, farmers can better understand the needs of the fields and cultivated plants on a micro-scale, thereby saving resources and putting less strain on our environment. The relative salinity of our soils is an important aspect because of the impact on production costs and yield. The future of site-specific crop production is moving towards a sensor-based on-the-go measurement approach because obtaining important soil characteristics quickly and cheaply is still one of the biggest challenges in precision agriculture today. Measuring soil electrical conductivity (EC) could offer an opportunity to overcome these limitations if the different salt components of soil could be separated by analytical methods. In our study, we present a calibration model based on conductometry with which the selective potassium and calcium content can be determined in the laboratory under controlled conditions. Solutions containing K+ and Ca2+ cations in the concentration determined in the experimental model were mixed and measured by changing the frequency of the measuring current. In this study, measurements proved that a mathematical relationship can be used to describe the relationship between the composition and concentration of the two-component solution, the measurement frequency and the conductivity. The potassium (K) and calcium (Ca) content of the solution can be separated from each other, and a regression calibration curve can be recorded, from which the proportion of potassium and calcium in the given solution can be determined as a function

On the error term in Weyl's law for the Heisenberg manifolds (II)

In this paper we study the mean square of the error term in the Weyl's law of an irrational $(2l+1)$-dimensional Heisenberg manifold . An asymptotic formula is established

30 years of collaboration

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gaveat the Joint Austrian-Hungarian Mathematical Conference 2015, August 25-27, 2015 in Győr (Hungary)

Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Chronic escitalopram treatment attenuated the accelerated rapid eye movement sleep transitions after selective rapid eye movement sleep deprivation: a model-based analysis using Markov chains

BackgroundShortened rapid eye movement (REM) sleep latency and increased REM sleep amount are presumed biological markers of depression. These sleep alterations are also observable in several animal models of depression as well as during the rebound sleep after selective REM sleep deprivation (RD). Furthermore, REM sleep fragmentation is typically associated with stress procedures and anxiety. The selective serotonin reuptake inhibitor (SSRI) antidepressants reduce REM sleep time and increase REM latency after acute dosing in normal condition and even during REM rebound following RD. However, their therapeutic outcome evolves only after weeks of treatment, and the effects of chronic treatment in REM-deprived animals have not been studied yet.ResultsChronic escitalopram- (10 mg/kg/day, osmotic minipump for 24 days) or vehicle-treated rats were subjected to a 3-day-long RD on day 21 using the flower pot procedure or kept in home cage. On day 24, fronto-parietal electroencephalogram, electromyogram and motility were recorded in the first 2 h of the passive phase. The observed sleep patterns were characterized applying standard sleep metrics, by modelling the transitions between sleep phases using Markov chains and by spectral analysis.Based on Markov chain analysis, chronic escitalopram treatment attenuated the REM sleep fragmentation [accelerated transition rates between REM and non-REM (NREM) stages, decreased REM sleep residence time between two transitions] during the rebound sleep. Additionally, the antidepressant avoided the frequent awakenings during the first 30 min of recovery period. The spectral analysis showed that the SSRI prevented the RD-caused elevation in theta (5 inverted question mark9 Hz) power during slow-wave sleep. Conversely, based on the aggregate sleep metrics, escitalopram had only moderate effects and it did not significantly attenuate the REM rebound after RD.ConclusionIn conclusion, chronic SSRI treatment is capable of reducing several effects on sleep which might be the consequence of the sub-chronic stress caused by the flower pot method. These data might support the antidepressant activity of SSRIs, and may allude that investigating the rebound period following the flower pot protocol could be useful to detect antidepressant drug response. Markov analysis is a suitable method to study the sleep pattern

Acute escitalopram treatment inhibits REM sleep rebound and activation of MCH-expressing neurons in the lateral hypothalamus after long term selective REM sleep deprivation.

RATIONALE: Selective rapid eye movement sleep (REMS) deprivation using the platform-on-water ("flower pot") method causes sleep rebound with increased REMS, decreased REMS latency, and activation of the melanin-concentrating hormone (MCH) expressing neurons in the hypothalamus. MCH is implicated in the pathomechanism of depression regarding its influence on mood, feeding behavior, and REMS. OBJECTIVES: We investigated the effects of the most selective serotonin reuptake inhibitor escitalopram on sleep rebound following REMS deprivation and, in parallel, on the activation of MCH-containing neurons. METHODS: Escitalopram or vehicle (10 mg/kg, intraperitoneally) was administered to REMS-deprived (72 h) or home cage male Wistar rats. During the 3-h-long "rebound sleep", electroencephalography was recorded, followed by an MCH/Fos double immunohistochemistry. RESULTS: During REMS rebound, the time spent in REMS and the number of MCH/Fos double-labeled neurons in the lateral hypothalamus increased markedly, and REMS latency showed a significant decrease. All these effects of REMS deprivation were significantly attenuated by escitalopram treatment. Besides the REMS-suppressing effects, escitalopram caused an increase in amount of and decrease in latency of slow wave sleep during the rebound. CONCLUSIONS: These results show that despite the high REMS pressure caused by REMS deprivation procedure, escitalopram has the ability to suppress REMS rebound, as well as to diminish the activation of MCH-containing neurons, in parallel. Escitalopram caused a shift from REMS to slow wave sleep during the rebound. Furthermore, these data point to the potential connection between the serotonergic system and MCH in sleep regulation, which can be relevant in depression and in other mood disorders

Nesfatin-1/NUCB2 as a Potential New Element of Sleep Regulation in Rats.

STUDY OBJECTIVES: Millions suffer from sleep disorders that often accompany severe illnesses such as major depression; a leading psychiatric disorder characterized by appetite and rapid eye movement sleep (REMS) abnormalities. Melanin-concentrating hormone (MCH) and nesfatin-1/NUCB2 (nesfatin) are strongly co - expressed in the hypothalamus and are involved both in food intake regulation and depression. Since MCH was recognized earlier as a hypnogenic factor, we analyzed the potential role of nesfatin on vigilance. DESIGN: We subjected rats to a 72 h-long REMS deprivation using the classic flower pot method, followed by a 3 h-long 'rebound sleep'. Nesfatin mRNA and protein expressions as well as neuronal activity (Fos) were measured by quantitative in situ hybridization technique, ELISA and immunohistochemistry, respectively, in 'deprived' and 'rebound' groups, relative to controls sacrificed at the same time. We also analyzed electroencephalogram of rats treated by intracerebroventricularly administered nesfatin-1, or saline. RESULTS: REMS deprivation downregulated the expression of nesfatin (mRNA and protein), however, enhanced REMS during 'rebound' reversed this to control levels. Additionally, increased transcriptional activity (Fos) was demonstrated in nesfatin neurons during 'rebound'. Centrally administered nesfatin-1 at light on reduced REMS and intermediate stage of sleep, while increased passive wake for several hours and also caused a short-term increase in light slow wave sleep. CONCLUSIONS: The data designate nesfatin as a potential new factor in sleep regulation, which fact can also be relevant in the better understanding of the role of nesfatin in the pathomechanism of depression

Spacings between selected prime divisors of an integer

Given a large integer n, determining the relative size of each of its prime divisors as well as the spacings between these prime divisors has been the focus of several studies. Here, we examine the spacings between particular types of prime divisors of n, such as certain congruence classes of primes and various other subsets of the set of prime numbers