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This study investigates a number of integrals possessing products of different indices of the univariate Lommel function, sμ,ν(a){s}_{\mu ,\nu }\left(a), with various elementary and special functions. As a consequence, connections between the function and Chebyshev polynomials of the first kind are established.

This paper aims to show how some standard general results can be used to uncover the spectral theory of tridiagonal and related matrices more elegantly and simply than existing approaches. As a typical example, we apply the theory to the special tridiagonal matrices in recent papers on orthogonal polynomials arising from Jordan blocks. Consequently, we find that the polynomials and spectral theory of the special matrices are expressible in terms of the Chebyshev polynomials of second kind, whose properties yield interesting results. For special cases, we obtain results in terms of the Fibonacci numbers and Legendre polynomials.

In this paper, we disprove a remaining conjecture about Bohemian matrices, in which the numbers of distinct determinants of a normalized Bohemian upper-Hessenberg matrix were conjectured.

In this note, we recall several connections between the determinant of some tridiagonal matrices and the orthogonal polynomials allowing the relation between Chebyshev polynomials of second kind and Fibonacci numbers. With basic transformations, we are able to recover some recent results on this matter, bringing them into one place.

Let A be a real symmetric matrix. If after we delete a row and a column of the same index, the nullity increases by one, we call that index a P-vertex of A. When A is an n × n singular acyclic matrix, it is known that the maximum number of P-vertices is n − 2. If T is the underlying tree of A, we will show that for any integer number k ∈ {0, 1, . . . , n − 2}, there is a (singular) matrix whose graph is T and with k P-vertices. We will provide illustrative examples.

Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix related to some Lie Algebras. The determinant of an extension of that matrix is presented.

In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.

In this work we show that the Bruhat rank of a symmetric (0,1)-matrix of order n with a staircase pattern, total support, and containing In, is at most 2. Several other related questions are also discussed. Some illustrative examples are presented.

Therapies for the treatment of pain and inflammation continue to pose a global challenge, emphasizing the significant impact of pain on patients' quality of life. Therefore, this study aimed to investigate the effects of 4-(Phenylselanyl)-2H-chromen-2-one (4-PSCO) on pain-associated proteins through computational molecular docking tests. A new pharmaceutical formulation based on polymeric nanocapsules was developed and characterized. The potential toxicity of 4-PSCO was assessed using Caenorhabditis elegans and Swiss mice, and its pharmacological actions through acute nociception and inflammation tests were also assessed. Our results demonstrated that 4-PSCO, in its free form, exhibited high affinity for the selected receptors, including p38 MAP kinase, peptidyl arginine deiminase type 4, phosphoinositide 3-kinase, Janus kinase 2, toll-like receptor 4, and nuclear factor-kappa β. Both free and nanoencapsulated 4-PSCO showed no toxicity in nematodes and mice. Parameters related to oxidative stress and plasma markers showed no significant change. Both treatments demonstrated antinociceptive and anti-edematogenic effects in the glutamate and hot plate tests. The nanoencapsulated form exhibited a more prolonged effect, reducing mechanical hypersensitivity in an inflammatory pain model. These findings underscore the promising potential of 4-PSCO as an alternative for the development of more effective and safer drugs for the treatment of pain and inflammation.

In the present study, the effect of 6-((4-fluorophenyl) selanyl)-9H-purine (FSP) was tested against memory impairment and sensitivity to nociception induced by intracerebroventricular injection of amyloid-beta peptide (Aβ) (25-35 fragment), 3 nmol/3 μl/per site in mice. Memory impairment was determined by the object recognition task (ORT) and nociception by the Von-Frey test (VFT). Aβ caused neuroinflammation with upregulation of glial fibrillary acidic protein (GFAP) (in hippocampus), nuclear factor-κB (NF-κB), and the proinflammatory cytokines interferon-γ (IFN-γ) and tumor necrosis factor-α (TNF-α) in cerebral cortex and hippocampus. Additionally, Aβ increased oxidant levels and lipid peroxidation in cerebral cortex and hippocampus, but decreased heme oxygenase-1 (HO-1) and peroxiredoxin-1 (Prdx1) expression in the hippocampus. Anti-neuroinflammatory effects of FSP were demonstrated by a decrease in the expression of GFAP and NF-κB in the hippocampus, as well as a decrease in proinflammatory cytokines in both the hippocampus and cerebral cortex FSP protected against oxidative stress by decreasing oxidant levels and lipid peroxidation and by increasing HO-1 and Prdx1 expressions in the hippocampus of mice. Moreover, FSP prevented the activation of nuclear factor erythroid 2-related factor 2 (Nrf-2) in the hippocampus of mice induced by Aβ. In conclusion, treatment with FSP attenuated memory impairment, nociception sensitivity by decreasing oxidative stress, and neuroinflammation in a mouse model of Alzheimer's disease., (© 2022. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

Suppressive effect of bis (3-amino-2-pyridine) diselenide (BAPD) on psychiatric disorders - atopic dermatitis (AD) comorbidity in mice was investigated. To sensitize the animals, 2,4-dinitrochlorobenzene (DNCB) was applied to their dorsal skin on days 1-3. Mice were challenged with DNCB on their ears and dorsal skin on days 14, 17, 20, 23, 26, and 29. BAPD and Dexamethasone were administered to the animals, from days 14-29, and skin severity scores and behavioral tests were determined. Oxidative stress and inflammatory parameters were evaluated on the dorsal skin of mice. Na + , K + -ATPase activity and corticosterone levels were determined in hippocampus/cerebral cortex and plasma of mice, respectively. BAPD improved cutaneous damage, scratching behavior, inflammatory and oxidative stress markers. BAPD showed anxiolytic- and antidepressant-like effects and restored Na + , K + -ATPase activity and corticosterone levels. The present study was performed using female mice due the susceptibility for this disease. But, the evaluation of AD model in male mice would help to verify whether the male gender has the same predisposition to present this pathology. Our data demonstrated the suppressive effect of BAPD on psychiatric disorders - AD comorbidity by regulating inflammatory and oxidative status in mice., (Copyright © 2021 Elsevier B.V. All rights reserved.)

Recently, we demonstrated the promising anxiolytic action of 7-chloro-4-(phenylselanyl) quinoline (4-PSQ) in mice. For this reason, the objective of this study was to expand our previous findings by investigating the contribution of serotoninergic and GABAergic systems to the anxiolytic action of this compound. Pretreatment with different serotoninergic antagonists (pindolol, WAY100635 and ketanserin) blocked the anxiolytic effect caused by 4-PSQ (50 mg/kg, per oral) in the elevated plus maze (EPM) test. The contribution of the GABAergic system was investigated by pretreatment with pentylenetetrazole (a GABA A receptor antagonist) (PTZ). 4-PSQ diminished the PTZ-induced anxiety, and did not modify the locomotor, exploratory and motor activities of mice. Later, this group of animals was euthanized and the blood was removed to determine the levels of corticosterone, and cerebral cortex and hippocampus to determine the mRNA expression levels of cAMP response element binding protein (CREB), brain derived neurotrophic factor (BDNF) and nuclear factor kappa B (NF-κB), as well as the Na + , K + ATPase activity and reactive species (RS) levels. 4-PSQ was able to significantly reverse the increase in RS and corticosterone levels, as well as the decrease of CREB and BDNF expression in the cerebral structures and increase of NF-κB expression in the hippocampus. Finally, 4-PSQ restored the Na + , K + ATPase activity in the cerebral structures evaluated. Here, we showed that the modulation of serotonergic and GABAergic systems, factors related to neurogenesis, oxidative status and Na + , K + ATPase activity contributes to the anxiolytic effect of 4-PSQ and reinforces the therapeutical potential of this compound for the treatment of anxiety., Competing Interests: Declaration of Competing Interest The authors declare that they have no conflict of interest., (Copyright © 2020 Elsevier B.V. All rights reserved.)

Background: The present study evaluated the antioxidant, antinociceptive and anti-edematogenic effects of Se-[(2,2-dimethyl-1,3-dioxolan-4-yl) methyl] 4-chlorobenzoselenolate (Se-DMC)., Methods: In vitro experiments were carried out to evaluate Se-DMC antioxidant action. Thiobarbituric acid reactive species levels, 2,2'-diphenyl-1-picrylhydrazyl and 2,2'-azino-bis(3-thylbenzthiazoline-6-sulfonic acid) radicals scavenging and glutathione S-transferase-like activity were determined. Male Swiss mice were orally pretreated with Se-DMC (1, 10 and 50 mg/kg), meloxicam (50 mg/kg) or vehicle 30 min prior to acetic acid or glutamate test. To extend our knowledge of the pharmacological properties of this compound, it was tested in an inflammatory model through ear edema induced by croton oil. The contribution of glutamatergic and serotonergic systems was also investigated., Results: In vitro experiments revealed that Se-DMC exerts antioxidant activity. Nociception induced by glutamate or acetic acid was reduced by Se-DMC or meloxicam. Se-DMC diminished the paw edema formation induced by glutamate, while meloxicam did not show any effect. Se-DMC and meloxicam decreased the ear edema formation and protected against the increase in myeloperoxidase activity in mice ear induced by croton oil. The pretreatment of animals with MK-801 did not alter antinociception caused by Se-DMC in the glutamate test. The antinociceptive effect exerted by Se-DMC in the acetic acid test was reverted by the pretreatment of mice with different serotonergic antagonists (WAY100635, ketanserin and pindolol)., Conclusions: Data presented here showed that the modulation of serotonergic and glutamatergic systems and the anti-inflammatory and antioxidant actions could contribute to the antinociceptive and anti-edematogenic effects of Se-DMC and it supported the therapeutic potential of this compound., (Copyright © 2019 Institute of Pharmacology, Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.)

Preclinical assays play a key role in research in research on the neurobiology of pain and the development of novel analgesics. Drugs available for the treatment of inflammatory pain are not fully effective and show adverse effects. Thus, we investigated the antinociceptive, anti-inflammatory and anti-hyperalgesic effects of bis(3-amino-2-pyridine) diselenide (BAPD), a new analgesic drug prototype. BAPD effects were investigated using nociception models induced by chemical (glutamate), immunologic (Freund's Complete Adjuvant - CFA) and thermal stimuli in Swiss mice. Mice were orally (p.o.) treated with BAPD (0.1-50 mg/kg) 30 min prior to the glutamate and hot-plate tests and a time-course (0.5 up to 8 h) of the antinociceptive effect of BAPD (50 mg/kg, p. o.) was evaluated in a CFA model. In the CFA model, BAPD effects on cyclooxygenase-2 (COX-2), tumor necrosis factor (TNFα) and interferon-γ (INF-γ) expression, myeloperoxidase (MPO) activity, oxidative (2,2'-Azino-bis-3-ethylbenzothiazoline 6-sulfonic acid and 2,2-diphe- nyl-1-picrylhydrazyl levels) and histological parameters were evaluated. The safety of the compound (50 and 300 mg/kg, p. o.) was verified for 72 h. BAPD reduced the licking time induced by glutamate and caused an increase in latency response to thermal stimulus. Naloxone reversed the antinociceptive effect of BAPD. Paw edema formation induced by glutamate or CFA injection was reduced by BAPD. Mechanical hyperalgesia induced by CFA was attenuated by BAPD. BAPD did not protect against the increase in MPO activity and decrease of the 2,2'-Azino-bis-3-ethylbenzothiazoline 6-sulfonic acid and 2,2-diphe- nyl-1-picrylhydrazyl levels induced by CFA. BAPD protected against histological alterations and reduction on the levels of gene expression COX-2 and INF-γ in the paw of mice exposed to CFA. BAPD was safe at the doses and time evaluated. BAPD exerts acute antinociceptive, anti-inflammatory and anti-hyperalgesic actions, suggesting that it may represent an alternative in the future development of new therapeutic strategies., (Copyright © 2019 Elsevier B.V. All rights reserved.)

Purpose: Determining the post-mortem interval (PMI) is one of the challenging tasks in forensic science due to the lack of quick and inexpensive methods. Our objective is to develop innovative and alternative means for PMI evaluation. Methods: The relationship between PMI and enzymatic modifications in mice tissues was described. After being sacrificed, Swiss mice were randomly divided into groups according to the time elapsed since death. The activities of catalase (CAT) and δ-aminolevulinate dehydratase (δ-ALA-D) were determined in hepatic, renal, skeletal muscle and cerebral tissues. Results: CAT activity increased in kidney and brain 6 h after death and this increase remained for up to 24 h in the brain and 48 h in the kidney. δ-ALA-D had its activity decreased in the liver and kidneys in 6 h. In the skeletal muscle, δ-ALA-D activity was reduced only 48 h after death. Conversely, an increase on δ-ALA-D activity was observed in the brain at 6 h, followed by its decrease at 24 and 48 h. Conclusion: With the association of this set of results, it is possible to provide an estimate of PMI. Additionally, these results can be used as an auxiliary parameter associated with other methods to estimate PMI.

Determining precisely the postmortem interval (PMI) is a key parameter for forensic researches, given that various physical, biochemical and metabolic changes begin to occur in the body after death. In the present study, the Na + /K + -ATPase, glutathione S-transferase (GST) and acetylcholinesterase (AChE) activities were evaluated. For this, male adult Swiss mice were killed by isoflurane inhalation anesthesia and divided into four groups according to time of death (0, 6, 24 and 48 h). The brain, liver, kidney and skeletal muscle tissues were removed. Our results revealed that at the time of 6 h, there was a decrease on Na + /K + -ATPase and GST activities in the brain and liver tissues, respectively. In addition, at this time point, an increase on renal GST activity was verified. At the time of 24 h, an increase on the cerebral AChE and renal GST activities was observed, while the cerebral Na + /K + -ATPase activity was decreased. Forty-eight hours after death, cerebral Na + /K + -ATPase and renal GST activities remained decreased and increased, respectively. In addition, no alteration was observed on the GST activity in the skeletal muscle and brain (in PMIs evaluated). The present study revealed that the brain and kidney (at the times of 24 and 48 h) were the tissues that suffered the most changes in almost all the enzymes evaluated. Our results demonstrated that enzyme activity assessments are reliable, easy-to-perform and low-cost determinations, and could be promising postmortem markers., (Copyright © 2018 Elsevier B.V. All rights reserved.)

A new quinoline containing selenium, 4-phenylselenyl-7-chloroquinoline (4-PSQ), was described and synthetized by our research group. Recently, we demonstrated the potential antinociceptive and anti-inflammatory of 4-PSQ. For this reason, the first objective of this study was to expand our previous findings by investigating the contribution of glutamatergic, serotonergic, and nitrergic systems to the acute antinociceptive action of this compound. Pretreatment with 4-PSQ (0.01-25 mg/kg, p.o.) reduced the nociception induced by glutamate. MK-801 (an uncompetitive antagonist of the N-Methyl-d-aspartate (NMDA) receptor) blocked the antinociceptive effect exerted by 4-PSQ (25 mg/kg, p.o.) in the acetic acid-induced abdominal writhing test. The pretreatment with WAY100635 (a selective antagonist of 5-HT 1A receptor), ketanserin (a selective antagonist of 5-HT 2A/2C receptor), and pindolol (a nonselective antagonist of 5-HT 1A/1B receptors) partially blocked the antinociceptive effect caused by 4-PSQ (25 mg/kg, per oral, p.o.) in the acetic acid-induced abdominal writhing test. Nitric oxide precursor, l-arginine hydrochloride, partially reversed antinociception caused by 4-PSQ or ω-nitro-l-arginine (l-NOARG). Treatments did not modify the locomotor and exploratory activities of mice. Additionally, the acute anti-inflammatory effect of 4-PSQ in a model of pleurisy induced by carrageenan in mice was investigated. 4-PSQ reduced the cellular migration, pleural exudate accumulation, and myeloperoxidase activity induced by carrageenan exposure. 4-PSQ protected against the increase in reactive species levels and reduction of nonprotein thiol levels induced by carrageenan. Data presented here showed that the modulation of serotonergic, nitrergic, and glutamatergic systems contributed to the antinociceptive effect of 4-PSQ and it reinforced the therapeutic potential of this quinolinic compound for acute inflammation., (© 2017 Société Française de Pharmacologie et de Thérapeutique.)