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The objective of this paper is to present several inequalities between the angles of a triangle and the sides based on Jordan's inequality, 2[pi] / x < sin x < x, for every x [member of] (0,[pi] / 2). Keywords Geometric inequality, triangle. Mathematics Subject Classification (2010): 26D15, 51M16., [section]1. Introduction In this paper, we will study the inequalities of type f(a,b,c,A,B,C,r,s,R,[DELTA]) [greater than or equal to] 0, in an acute triangle ABC, where a,b,c are the lenghts of [...]

ABSTRACT Some Smarandache relationships between the terms of a given sequence are studied in the first paragraph. In the second paragraph, are studied Smarandache subsequences (whose terms have the same [...]

In the paper, our main aim is to generalize the qth dual volume to Lp space, and introduce pqth-dual mixed volume by calculating the first order variation of qth dual volumes. We establish the Lpq-Minkowski inequality for pqth-dual mixed volumes and Lpq-Brunn-Minkowski inequality for the qth-dual volumes, respectively. The new inequalities in special case yield some new dual inequalities for the qth-dual volumes.

In the paper, Lp-harmonic addition, p-harmonic Blaschke addition and Lp-dual mixed volume are improved. A new p-harmonic Blaschke mixed quermassintegral is introduced. The relationship between p-harmonic Blaschke mixed volume and Lp-dual mixed volume is shown.

In the paper, the concept of Lp-dual three-mixed quermassintegrals is introduced. The formula for the Lp-dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of Lp-Minkowski, and Brunn-Minkowski type for the Lp-dual three-mixed quermassintegrals are established. The new Lp-Minkowski inequality is obtained that generalize a family of Minkowski type inequalities. The Lp-Brunn-Minkowski inequality is used to obtain a series of Brunn-Minkowski type inequalities.

If A is a rectangular matrix of rank r, then A may be written as PSQ where P and Q are invertible matrices and s=(IrOOO)s = \left( {\matrix{ \hfill {{{\rm{I}}_{\rm{r}}}} & \hfill {\rm{O}} \cr \hfill {\rm{O}} & \hfill {\rm{O}} \cr } } \right). This is the rank normal form of the matrix A.

The duration of denture use, oral hygiene, smoking and male sex were identified as risk factors for oral mucosal lesions. As it is well known, all the oral mucosal lesions associated with risk factors have an important degree of malignity. Chronic mechanical irritation can be another cause of oral cancer and it is produced by the constant action of a deleterious agent from the oral cavity. Autophagy represents a complex evolutionary conserved catabolic process in which cells self-digest intracellular organelles in order to regulate their normal turnover and remove the damaged ones with compromised function to further maintain homeostasis. Autophagy is modulated by mTOR kinase and indirectly by PI3K/AKT survival pathway. Due to its dual capacity to either induce cell death or promote cell survival, important evidence pointed that autophagy has a two-faced role in response to chemotherapy in cancer. In conclusion, understanding how to overcome cytoprotective autophagy and how to take advantage of autophagic cell death is critical in order to enhance the cancer cells sensitivity to particular therapeutic agents.

In this paper we present some results about k-perfect numbers, and generalize two inequalities due to M. Perisastri (see [6]).

In this paper we prove some results concerning bicentric quadrilaterals. We offer a new proof of the Blundon-Eddy inequality, which we use to obtain other inequalities in bicentric quadrilaterals.

Abstract The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two parameters are studied, the main result is then used to obtain several interesting and significantly inequalities for generalized Heronian means.

We hypothesized that sympathetic hyperactivity and parasympathetic insuficiency in spontaneously hypertensive rats (SHR) underlie their exaggerated cardiovascular response to acute stress and impaired adaptation to repeated restraint stress exposure compared to Wistar-Kyoto rats (WKY). Cardiovascular responses to single (120 min) or repeated (daily 120 min for 1 week) restraint were measured by radiotelemetry and autonomic balance was evaluated by power spectral analysis of systolic blood pressure variability (SBPV) and heart rate variability (HRV). Baroreflex sensitivity (BRS) was measured by the pharmacological Oxford technique. Stress-induced pressor response and vascular sympathetic activity (low-frequency component of SBPV) were enhanced in SHR subjected to single restraint compared to WKY, whereas stress-induced tachycardia was similar in both strains. SHR exhibited attenuated cardiac parasympathetic activity (high-frequency component of HRV) and blunted BRS compared to WKY. Repeated restraint did not affect the stress-induced increase in blood pressure. However, cardiovascular response during the post-stress recovery period of the 7th restraint was reduced in both strains. The repeatedly restrained SHR showed lower basal heart rate during the dark (active) phase and slightly decreased basal blood pressure during the light phase compared to stress-naive SHR. SHR subjected to repeated restraint also exhibited attenuated stress-induced tachycardia, augmented cardiac parasympathetic activity, attenuated vascular sympathetic activity and improved BRS during the last seventh restraint compared to single-stressed SHR. Thus, SHR exhibited enhanced cardiovascular and sympathetic responsiveness to novel stressor exposure (single restraint) compared to WKY. Unexpectedly, the adaptation of cardiovascular and autonomic responses to repeated restraint was more effective in SHR., (© 2024. The Author(s).)

Spontaneously hypertensive rats (SHR) are characterized by sympathetic hyperactivity and insufficient parasympathetic activity, and their high blood pressure (BP) can be lowered by long-term inhibition of the renin-angiotensin system. The aim of our study was to determine the influence of chronic inhibition of angiotensin converting enzyme (ACE) by captopril on cardiovascular regulation by the sympathetic and parasympathetic nervous system. Implanted radiotelemetric probes or arterial cannulas were used to measure mean arterial pressure (MAP), heart rate (HR), and arterial baroreflex in adult SHR and Wistar-Kyoto (WKY) rats under basal or stress conditions. MAP and the low-frequency component of systolic blood pressure variability (LF-SBPV, marker of sympathetic activity) were greater in SHR than in WKY rats. Under basal conditions chronic captopril treatment reduced both parameters more effectively in SHR, and the same was true during acute restraint stress. HR was similar in control rats of both strains, but WKY rats showed greater heart rate variability (HRV), indicating higher parasympathetic activity. Captopril administration increased HR in both strains, whereas HRV was decreased only in WKY. Chronic captopril treatment improved the impaired baroreflex-HR control in SHR by increasing the sensitivity but not the capacity of vagal arm of arterial baroreflex. Captopril treatment attenuated BP changes elicited by dimethylphenylpiperazinium (DMPP, agonist of nicotinic acetylcholine receptors), especially in SHR, indicating that sympathetic nerve transmission is facilitated by angiotensin II more in hypertensive than in normotensive animals. Thus, chronic ACE inhibition improves baroreflex sensitivity and lowers BP through both central and peripheral attenuation of sympathetic tone., Competing Interests: Declaration of Competing Interest The authors declare no conflicts of interest., (Copyright © 2024 The Authors. Published by Elsevier Masson SAS.. All rights reserved.)

Chronic treatment with acetylcholinesterase inhibitors may be a promising therapeutic strategy for treatment of cardiovascular diseases. The aim of our study was to analyze the changes in blood pressure (BP) and heart rate (HR) during 14 days of treatment with two different acetylcholinesterase inhibitors - pyridostigmine (PYR) having only peripheral effects or donepezil (DON) with both peripheral and central effects. In addition, we studied their effects on the cardiovascular response to restraint stress and on sympathovagal control of HR in normotensive Wistar-Kyoto rats (WKY) and spontaneously hypertensive rats (SHR). SHR were characterized by elevated BP and increased low-frequency component of systolic BP variability (LF-SBPV), but their cardiac vagal tone and HR variability (HRV) were reduced compared with WKY. Chronic treatment with either acetylcholinesterase inhibitor decreased HR and increased HRV in both strains. PYR treatment slightly decreased BP and LF-SBPV in the dark phase of the day. Neither drug significantly altered BP response to stress, but PYR attenuated HR increase during restraint stress. Regarding sympathovagal balance, acute methylatropine administration caused a greater increase of HR in WKY than in SHR. Chronic PYR or DON treatment enhanced HRV and HR response to methylatropine (vagal tone) in WKY, whereas PYR but not DON treatment potentiated HRV and vagal tone in SHR. In conclusion, vagal tone was lower in SHR compared with WKY, but was enhanced by chronic PYR treatment in both strains. Thus, chronic peripheral, but not central, acetylcholinesterase inhibition has major effects on HR and its variability in both normotensive and hypertensive rats., Competing Interests: Declaration of competing interest There is no conflict of interest., (Copyright © 2024 The Authors. Published by Elsevier B.V. All rights reserved.)

Background: Duchenne muscular dystrophy (DMD) is a progressive muscle degenerative disorder, culminating in a complete loss of ambulation, hypertrophic cardiomyopathy and a fatal cardiorespiratory failure. Necroptosis is the form of necrosis that is dependent upon the receptor-interacting protein kinase (RIPK) 3; it is involved in several inflammatory and neurodegenerative conditions. We previously identified RIPK3 as a key player in the acute myonecrosis affecting the hindlimb muscles of the mdx dystrophic mouse model. Whether necroptosis also mediates respiratory and heart disorders in DMD is currently unknown., Methods: Evidence of activation of the necroptotic axis was examined in dystrophic tissues from Golden retriever muscular dystrophy (GRMD) dogs and R-DMDdel52 rats. A functional assessment of the involvement of necroptosis in dystrophic animals was performed on mdx mice that were genetically depleted for RIPK3. Dystrophic mice aged from 12 to 18 months were analysed by histology and molecular biology to compare the phenotype of muscles from mdxRipk3 +/+ and mdxRipk3 -/- mice. Heart function was also examined by echocardiography in 40-week-old mice., Results: RIPK3 expression in sartorius and biceps femoris muscles from GRMD dogs positively correlated to myonecrosis levels (r = 0.81; P = 0.0076). RIPK3 was also found elevated in the diaphragm (P ≤ 0.05). In the slow-progressing heart phenotype of GRMD dogs, the phosphorylated form of RIPK1 at the Serine 161 site was dramatically increased in cardiomyocytes. A similar p-RIPK1 upregulation characterized the cardiomyocytes of the severe DMDdel52 rat model, associated with a marked overexpression of Ripk1 (P = 0.007) and Ripk3 (P = 0.008), indicating primed activation of the necroptotic pathway in the dystrophic heart. MdxRipk3 -/- mice displayed decreased compensatory hypertrophy of the heart (P = 0.014), and echocardiography showed a 19% increase in the relative wall thickness (P < 0.05) and 29% reduction in the left ventricle mass (P = 0.0144). Besides, mdxRipk3 -/- mice presented no evidence of a regenerative default or sarcopenia in skeletal muscles, moreover around 50% less affected by fibrosis (P < 0.05)., Conclusions: Our data highlight molecular and histological evidence that the necroptotic pathway is activated in degenerative tissues from dystrophic animal models, including the diaphragm and the heart. We also provide the genetic proof of concept that selective inhibition of necroptosis in dystrophic condition improves both histological features of muscles and cardiac function, suggesting that prevention of necroptosis is susceptible to providing multiorgan beneficial effects for DMD., (© 2023 The Authors. Journal of Cachexia, Sarcopenia and Muscle published by John Wiley & Sons Ltd on behalf of Society on Sarcopenia, Cachexia and Wasting Disorders.)

Myofibre necrosis is a central pathogenic process in muscular dystrophies (MD). As post-lesional regeneration cannot fully compensate for chronic myofibre loss, interstitial tissue accumulates and impairs muscle function. Muscle regeneration has been extensively studied over the last decades, however, the pathway(s) controlling muscle necrosis remains largely unknown. The recent discovery of several regulated cell death (RCD) pathways with necrotic morphology challenged the dogma of necrosis as an uncontrolled process, opening interesting perspectives for many degenerative disorders. In this review, we focus on how cell death affects myofibres in MDs, integrating the latest research in the cell death field, with specific emphasis on Duchenne muscular dystrophy, the best-known and most common hereditary MD. The role of regulated forms of necrosis in myology is still in its infancy but there is increasing evidence that necroptosis, a genetically programmed form of necrosis, is involved in muscle degenerating disorders. The existence of apoptosis in myofibre demise will be questioned, while other forms of non-apoptotic RCDs may also have a role in myonecrosis, illustrating the complexity and possibly the heterogeneity of the cell death pathways in muscle degenerating conditions.

Background: Facioscapulohumeral dystrophy (FSHD) is caused by mutations leading to the aberrant expression of the DUX4 transcription factor in muscles. DUX4 was proposed to induce cell death, but the involvement of different death pathways is still discussed. A possible pro-apoptotic role of DUX4 was proposed, but as FSHD muscles are characterized by necrosis and inflammatory infiltrates, non-apoptotic pathways may be also involved., Methods: We explored DUX4-mediated cell death by focusing on the role of one regulated necrosis pathway called necroptosis, which is regulated by RIPK3. We investigated the effect of necroptosis on cell death in vitro and in vivo experiments using RIPK3 inhibitors and a RIPK3-deficient transgenic mouse model., Results: We showed in vitro that DUX4 expression causes a caspase-independent and RIPK3-mediated cell death in both myoblasts and myotubes. In vivo, RIPK3-deficient animals present improved body and muscle weights, a reduction of the aberrant activation of the DUX4 network genes, and an improvement of muscle histology., Conclusions: These results provide evidence for a role of RIPK3 in DUX4-mediated cell death and open new avenues of research., (© 2021 The Authors. Journal of Cachexia, Sarcopenia and Muscle published by John Wiley & Sons Ltd on behalf of Society on Sarcopenia, Cachexia and Wasting Disorders.)

Increased level of C-reactive protein (CRP) is a risk factor for cardiovascular diseases, including myocardial infarction and hypertension. Here, we analyzed the effects of CRP overexpression on cardiac susceptibility to ischemia/reperfusion (I/R) injury in adult spontaneously hypertensive rats (SHR) expressing human CRP transgene (SHR-CRP). Using an in vivo model of coronary artery occlusion, we found that transgenic expression of CRP predisposed SHR-CRP to repeated and prolonged ventricular tachyarrhythmias. Excessive ischemic arrhythmias in SHR-CRP led to a significant reduction in infarct size (IS) compared with SHR. The proarrhythmic phenotype in SHR-CRP was associated with altered heart and plasma eicosanoids, myocardial composition of fatty acids (FAs) in phospholipids, and autonomic nervous system imbalance before ischemia. To explain unexpected IS-limiting effect in SHR-CRP, we performed metabolomic analysis of plasma before and after ischemia. We also determined cardiac ischemic tolerance in hearts subjected to remote ischemic perconditioning (RIPer) and in hearts ex vivo. Acute ischemia in SHR-CRP markedly increased plasma levels of multiple potent cardioprotective molecules that could reduce IS at reperfusion. RIPer provided IS-limiting effect in SHR that was comparable with myocardial infarction observed in naïve SHR-CRP. In hearts ex vivo, IS did not differ between the strains, suggesting that extra-cardiac factors play a crucial role in protection. Our study shows that transgenic expression of human CRP predisposes SHR-CRP to excess ischemic ventricular tachyarrhythmias associated with a drop of pump function that triggers myocardial salvage against lethal I/R injury likely mediated by protective substances released to blood from hypoxic organs and tissue at reperfusion., (© 2021 The Author(s). Published by Portland Press Limited on behalf of the Biochemical Society.)

Background: Desmin is a muscle-specific protein belonging to the intermediate filament family. Desmin mutations are linked to skeletal muscle defects, including inherited myopathies with severe clinical manifestations. The aim of this study was to examine the role of desmin in skeletal muscle remodeling and performance gain induced by muscle mechanical overloading which mimics resistance training. Methods: Plantaris muscles were overloaded by surgical ablation of gastrocnemius and soleus muscles. The functional response of plantaris muscle to mechanical overloading in desmin-deficient mice ( Des KO, n = 32) was compared to that of control mice ( n = 36) after 7-days or 1-month overloading. To elucidate the molecular mechanisms implicated in the observed partial adaptive response of Des KO muscle, we examined the expression levels of genes involved in muscle growth, myogenesis, inflammation and oxidative energetic metabolism. Moreover, ultrastructure and the proteolysis pathway were explored. Results: Contrary to control, absolute maximal force did not increase in Des KO muscle following 1-month mechanical overloading. Fatigue resistance was also less increased in Des KO as compared to control muscle. Despite impaired functional adaptive response of Des KO mice to mechanical overloading, muscle weight and the number of oxidative MHC2a-positive fibers per cross-section similarly increased in both genotypes after 1-month overloading. However, mechanical overloading-elicited remodeling failed to activate a normal myogenic program after 7-days overloading, resulting in proportionally reduced activation and differentiation of muscle stem cells. Ultrastructural analysis of the plantaris muscle after 1-month overloading revealed muscle fiber damage in Des KO, as indicated by the loss of sarcomere integrity and mitochondrial abnormalities. Moreover, the observed accumulation of autophagosomes and lysosomes in Des KO muscle fibers could indicate a blockage of autophagy. To address this issue, two main proteolysis pathways, the ubiquitin-proteasome system and autophagy, were explored in Des KO and control muscle. Our results suggested an alteration of proteolysis pathways in Des KO muscle in response to mechanical overloading. Conclusion: Taken together, our results show that mechanical overloading increases the negative impact of the lack of desmin on myofibril organization and mitochondria. Furthermore, our results suggest that under these conditions, the repairing activity of autophagy is disturbed. Consequently, force generation is not improved despite muscle growth, suggesting that desmin is required for a complete response to resistance training in skeletal muscle., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer VM declared a past co- authorship with the authors ZL, OA to the handling editor., (Copyright © 2021 Joanne, Hovhannisyan, Bencze, Daher, Parlakian, Toutirais, Gao-Li, Lilienbaum, Li, Kordeli, Ferry and Agbulut.)

Most inherited neurodegenerative disorders are incurable, and often only palliative treatment is available. Precision medicine has great potential to address this unmet clinical need. We explored this paradigm in dopamine transporter deficiency syndrome (DTDS), caused by biallelic loss-of-function mutations in SLC6A3 , encoding the dopamine transporter (DAT). Patients present with early infantile hyperkinesia, severe progressive childhood parkinsonism, and raised cerebrospinal fluid dopamine metabolites. The absence of effective treatments and relentless disease course frequently leads to death in childhood. Using patient-derived induced pluripotent stem cells (iPSCs), we generated a midbrain dopaminergic (mDA) neuron model of DTDS that exhibited marked impairment of DAT activity, apoptotic neurodegeneration associated with TNFα-mediated inflammation, and dopamine toxicity. Partial restoration of DAT activity by the pharmacochaperone pifithrin-μ was mutation-specific. In contrast, lentiviral gene transfer of wild-type human SLC6A3 complementary DNA restored DAT activity and prevented neurodegeneration in all patient-derived mDA lines. To progress toward clinical translation, we used the knockout mouse model of DTDS that recapitulates human disease, exhibiting parkinsonism features, including tremor, bradykinesia, and premature death. Neonatal intracerebroventricular injection of human SLC6A3 using an adeno-associated virus (AAV) vector provided neuronal expression of human DAT, which ameliorated motor phenotype, life span, and neuronal survival in the substantia nigra and striatum, although off-target neurotoxic effects were seen at higher dosage. These were avoided with stereotactic delivery of AAV2.SLC6A3 gene therapy targeted to the midbrain of adult knockout mice, which rescued both motor phenotype and neurodegeneration, suggesting that targeted AAV gene therapy might be effective for patients with DTDS., (Copyright © 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

Lack of leptin production in ob/ob mice results in obesity and prediabetes that could be partly reversed by leptin supplementation. In the hypothalamus, leptin supports the production of prolactin-releasing peptide (PrRP), an anorexigenic neuropeptide synthesized and active in the brain. In our recent studies, the palmitoylated PrRP analog palm11-PrRP31 showed a central anorexigenic effect after peripheral administration. This study investigates whether PrRP could compensate for the deficient leptin in ob/ob mice. In two separate experiments, palm11-PrRP31 (5 mg/kg) and leptin (5 or 10 μg/kg) were administered subcutaneously twice daily for 2 or 8 weeks to 8- (younger) or 16-(older) week-old ob/ob mice, respectively, either separately or in combination. The body weight decreasing effect of palm11-PrRP31 in both younger and older ob/ob mice was significantly powered by a subthreshold leptin dose, the combined effect could be then considered synergistic. Leptin and palm11-PrRP31 also synergistically lowered liver weight and blood glucose in younger ob/ob mice. Reduced liver weight was linked to decreased mRNA expression of lipogenic enzymes. In the hypothalamus of older ob/ob mice, two main leptin anorexigenic signaling pathways, namely, Janus kinase, signal transducer and activator of transcription-3 activation and AMP-activated protein kinase de-activation, were induced by leptin, palm11-PrRP31, and their combination. Thus, palm11-PrRP31 could partially compensate for leptin deficiency in ob/ob mice. In conclusion, the results demonstrate a synergistic effect of leptin and our lipidized palm11-PrRP31 analog.

The necrosis of muscle fibres (myonecrosis) plays a central role in the pathogenesis of several muscle conditions, including muscular dystrophies. Therapeutic options addressing the causes of muscular dystrophy pathogenesis are expected to alleviate muscle degeneration. Therefore, a method to assay and quantify the extent of cell death in muscle biopsies is needed. Conventional methods to observe myofiber degeneration in situ are either poorly quantitative or rely on the injection of vital dyes. In this article, an immunofluorescence protocol is described that stains necrotic myofibers by targeting immunoglobulin G (IgG) uptake by myofibers. The IgG uptake method is based on cell features characterizing the necrotic demise, including 1) the loss of plasma membrane integrity with the release of damage-associated molecular patterns and 2) the uptake of plasmatic proteins. In murine cross-sections, the co-immunolabelling of myofibers, extracellular matrix proteins, and mouse IgG allows clean and straightforward identification of myofibers with necrotic fate. This simple method is suitable for quantitative analysis and applicable to all species, including human samples, and does not require the injection of vital dye. The staining of necrotic myofibers by IgG uptake can also be paired with other co-immunolabelling.

The effect of chemical sympathectomy on cardiovascular parameters and the compensatory role of adrenal hormones, the renin-angiotensin system, and cardiovascular sensitivity to vasoconstrictors were studied in spontaneously hypertensive rats (SHRs) and normotensive Wistar-Kyoto (WKY) rats. Sympathectomy was induced in 20-week-old rats by daily intraperitoneal guanethidine administration (30 mg/kg b.w.) for 2 weeks. Basal blood pressure (BP), heart rate (HR), and restraint stress-induced cardiovascular changes were measured by radiotelemetry. The BP response to catecholamines was determined in rats with implanted catheters. Sympathectomy decreased BP only transiently, and after 14-day guanethidine treatment, BP returned to basal values in both strains. Sympathectomy permanently lowered HR, improved baroreflex sensitivity, and decreased the low-frequency domain of systolic blood pressure variability (a marker of vascular sympathetic activity). Guanethidine also attenuated the BP and HR responses to restraint stress. On the other hand, the BP response to catecholamines was augmented in sympathectomized rats, and this was not due to the de novo synthesis of vascular adrenergic receptors. Sympathectomy caused adrenal enlargement, enhanced the expression of adrenal catecholamine biosynthetic enzymes, and elevated plasma adrenaline levels in both strains, especially in WKY rats. Guanethidine also increased the plasma levels of aldosterone and corticosterone in WKY rats only. In conclusion, sympathectomy produced a transient decrease in BP, a chronic decrease in HR and improvement in baroreflex sensitivity. The effect of sympathectomy on BP was counteracted by increased vascular sensitivity to catecholamines in WKY rats and SHRs and/or by the enhanced secretion of adrenal hormones, which was more pronounced in WKY rats.