Nonlinear Time-Fractional Differential Equations in Combustion Science

MSC 2010: 34A08 (main), 34G20, 80A25

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.

A Simple Example of Localized Parametric Resonance for the Wave Equation

2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Delayed and occult splenic rupture: a diagnostic puzzle

Splenic rupture is a common complaint encountered in emergency surgery. Trauma is the most common cause of splenic rupture, while non-traumatic or occult splenic rupture (OSR) is a rare condition. The differential diagnosis weighs on treatment that ranges between close monitoring, splenorrhaphy, splenic conservation and splenectomy. We report a case of an 63-year-old man presenting with acute atraumatic left upper quadrant pain. Preliminary diagnosis was subsequently determined to be a hematoma secondary to OSR. More accurate detailed history revealed a previous trauma, which occurred more than one year before and mimicked an OSR. Delayed and occult splenic rupture are as different diagnosis as different treatment. Even in emergency surgery, the key for a target therapeutic strategy should consider an accurate diagnostic time.

Differential effects of low-temperature inhibition on the propylene induced autocatalysis of ethylene production, respiration and ripening of 'Hayward' kiwifruit

Previous studies (Stavroulakis and Sfakiotakis, 1993) have shown an inhibition of propylene-induced ethylene production in kiwifruit below a critical temperature range of 11-14.8 degrees C. The aim of this research was to identify the biochemical basis of this inhibition in kiwifruit below 11-14.8 degrees C. 'Hayward' kiwifruit were treated with increasing propylene concentrations at 10 and 20 degrees C. Ethylene biosynthesis pathways and fruit ripening were investigated. Kiwifruit at 20 degrees C in air started autocatalysis of ethylene production and ripened after 19 d with a concomitant increase in respiration. Ethylene production and the respiration rise appeared earlier with increased propylene concentrations. Ripening proceeded immediately after propylene treatment, while ethylene autocatalysis needed a lag period of 24-72 h. The latter event was attributed to the delay found in the induction of 1-aminocyclopropane-1-carboxylate synthase (ACC synthase) activity and consequently to the delayed increase of l-aminocyclopropane l-carboxylic acid (ACC) content. In contrast propylene treatment induced 1-aminocyclopropane-1-carboxylate oxidase (ACC oxidase) activity with no lag period. Moreover, transcription of ACC synthase and ACC oxidase genes was active only in ethylene-producing kiwifruit at 20 degrees C. In contrast, treatment at 10 degrees C with propylene strongly inhibited ethylene production, which was attributed to the low activities of both ACC synthase and ACC oxidase as well as the low initial ACC level. Interestingly, fruit treated with propylene at 10 degrees C appeared to be able to transcribe the ACC oxidase but not the ACC synthase gene. However, propylene induced ripening of that fruit almost as rapidly as in the propylene-treated fruit at 20 degrees C. Respiration rate was increased together with propylene concentration. It is concluded that kiwifruit stored at 20 degrees C behaves as a typical climacteric fruit, while at 10 degrees C behaves like a non-climacteric fruit. We propose that the main reasons for the inhibition of the propylene induced (autocatalytic) ethylene production in kiwifruit at low temperature (less than or equal to 10 degrees C), are primarily the suppression of the propylene-induced ACC synthase gene expression and the possible post-transcriptional modification of ACC oxidase.

Differential effects of low-temperature inhibition on the propylene induced autocatalysis of ethylene production, respiration and ripening of 'Hayward' kiwifruit

Previous studies (Stavroulakis and Sfakiotakis, 1993) have shown an inhibition of propylene-induced ethylene production in kiwifruit below a critical temperature range of 11-14.8 degrees C. The aim of this research was to identify the biochemical basis of this inhibition in kiwifruit below 11-14.8 degrees C. 'Hayward' kiwifruit were treated with increasing propylene concentrations at 10 and 20 degrees C. Ethylene biosynthesis pathways and fruit ripening were investigated. Kiwifruit at 20 degrees C in air started autocatalysis of ethylene production and ripened after 19 d with a concomitant increase in respiration. Ethylene production and the respiration rise appeared earlier with increased propylene concentrations. Ripening proceeded immediately after propylene treatment, while ethylene autocatalysis needed a lag period of 24-72 h. The latter event was attributed to the delay found in the induction of 1-aminocyclopropane-1-carboxylate synthase (ACC synthase) activity and consequently to the delayed increase of l-aminocyclopropane l-carboxylic acid (ACC) content. In contrast propylene treatment induced 1-aminocyclopropane-1-carboxylate oxidase (ACC oxidase) activity with no lag period. Moreover, transcription of ACC synthase and ACC oxidase genes was active only in ethylene-producing kiwifruit at 20 degrees C. In contrast, treatment at 10 degrees C with propylene strongly inhibited ethylene production, which was attributed to the low activities of both ACC synthase and ACC oxidase as well as the low initial ACC level. Interestingly, fruit treated with propylene at 10 degrees C appeared to be able to transcribe the ACC oxidase but not the ACC synthase gene. However, propylene induced ripening of that fruit almost as rapidly as in the propylene-treated fruit at 20 degrees C. Respiration rate was increased together with propylene concentration. It is concluded that kiwifruit stored at 20 degrees C behaves as a typical climacteric fruit, while at 10 degrees C behaves like a non-climacteric fruit. We propose that the main reasons for the inhibition of the propylene induced (autocatalytic) ethylene production in kiwifruit at low temperature (less than or equal to 10 degrees C), are primarily the suppression of the propylene-induced ACC synthase gene expression and the possible post-transcriptional modification of ACC oxidase.

Sufficient conditions for the existence of heteroclinic solutions for Phi-Laplacian differential equations

In this paper we consider the second order discontinuous equation in the real line, (a(t)φ(u′(t)))′ = f(t,u(t),u′(t)), a.e.t∈R, u(-∞) = ν⁻, u(+∞)=ν⁺, with φ an increasing homeomorphism such that φ(0)=0 and φ(R)=R, a∈C(R,R\{0})∩C¹(R,R) with a(t)>0, or a(t)<0, for t∈R, f:R³→R a L¹-Carathéodory function and ν⁻,ν⁺∈R such that ν⁻<ν⁺. We point out that the existence of heteroclinic solutions is obtained without asymptotic or growth assumptions on the nonlinearities φ and f. Moreover, as far as we know, this result is even new when φ(y)=y, that is, for equation (a(t)u′(t))′=f(t,u(t),u′(t)), a.e.t∈R.

Dynamical models in neuroscience: the delay FitzHugh-Nagumo equation

Il primo modello matematico in grado di descrivere il prototipo di un sistema eccitabile assimilabile ad un neurone fu sviluppato da R. FitzHugh e J. Nagumo nel 1961. Tale modello, per quanto schematico, rappresenta un importante punto di partenza per la ricerca nell'ambito neuroscientifico delle dinamiche neuronali, ed è infatti capostipite di una serie di lavori che hanno puntato a migliorare l’accuratezza e la predicibilità dei modelli matematici per le scienze. L’elevato grado di complessità nello studio dei neuroni e delle dinamiche inter-neuronali comporta, tuttavia, che molte delle caratteristiche e delle potenzialità dell’ambito non siano ancora state comprese appieno. In questo lavoro verrà approfondito un modello ispirato al lavoro originale di FitzHugh e Nagumo. Tale modello presenta l’introduzione di un termine di self-coupling con ritardo temporale nel sistema di equazioni differenziali, diventa dunque rappresentativo di modelli di campo medio in grado di descrivere gli stati macroscopici di un ensemble di neuroni. L'introduzione del ritardo è funzionale ad una descrizione più realistica dei sistemi neuronali, e produce una dinamica più ricca e complessa rispetto a quella presente nella versione originale del modello. Sarà mostrata l'esistenza di una soluzione a ciclo limite nel modello che comprende il termine di ritardo temporale, ove tale soluzione non può essere interpretata nell’ambito delle biforcazioni di Hopf. Allo scopo di esplorare alcune delle caratteristiche basilari della modellizzazione del neurone, verrà principalmente utilizzata l’impostazione della teoria dei sistemi dinamici, integrando dove necessario con alcune nozioni provenienti dall’ambito fisiologico. In conclusione sarà riportata una sezione di approfondimento sulla integrazione numerica delle equazioni differenziali con ritardo.

Systemic Granulomatous Diseases Associated With Multiple Palpable Masses That May Involve The Breast: Case Presentation And An Approach To The Differential Diagnosis.

Palpable mass is a common complaint presented to the breast surgeon. It is very uncommon for patients to report breast mass associated with palpable masses in other superficial structures. When these masses are related to systemic granulomatous diseases, the diagnosis and initiation of specific therapy can be challenging. The purpose of this paper is to report a case initially assessed by the breast surgeon and ultimately diagnosed as granulomatous variant of T-cell lymphoma, and discuss the main systemic granulomatous diseases associated with palpable masses involving the breast.

Water Stress Reveals Differential Antioxidant Responses Of Tolerant And Non-tolerant Sugarcane Genotypes.

The biochemical responses of the enzymatic antioxidant system of a drought-tolerant cultivar (IACSP 94-2094) and a commercial cultivar in Brazil (IACSP 95-5000) grown under two levels of soil water restriction (70% and 30% Soil Available Water Content) were investigated. IACSP 94-2094 exhibited one additional active superoxide dismutase (Cu/Zn-SOD VI) isoenzyme in comparison to IACSP 95-5000, possibly contributing to the heightened response of IACSP 94-2094 to the induced stress. The total glutathione reductase (GR) activity increased substantially in IACSP 94-2094 under conditions of severe water stress; however, the appearance of a new GR isoenzyme and the disappearance of another isoenzyme were found not to be related to the stress response because the cultivars from both treatment groups (control and water restrictions) exhibited identical changes. Catalase (CAT) activity seems to have a more direct role in H2O2 detoxification under water stress condition and the shift in isoenzymes in the tolerant cultivar might have contributed to this response, which may be dependent upon the location where the excessive H2O2 is being produced under stress. The improved performance of IACSP 94-2094 under drought stress was associated with a more efficient antioxidant system response, particularly under conditions of mild stress.

Neural Mechanisms And Delayed Gastric Emptying Of Liquid Induced Through Acute Myocardial Infarction In Rats.

Background: In pathological situations, such as acute myocardial infarction, disorders of motility of the proximal gut can trigger symptoms like nausea and vomiting. Acute myocardial infarction delays gastric emptying (GE) of liquid in rats. Objective: Investigate the involvement of the vagus nerve, α 1-adrenoceptors, central nervous system GABAB receptors and also participation of paraventricular nucleus (PVN) of the hypothalamus in GE and gastric compliance (GC) in infarcted rats. Methods: Wistar rats, N = 8-15 in each group, were divided as INF group and sham (SH) group and subdivided. The infarction was performed through ligation of the left anterior descending coronary artery. GC was estimated with pressure-volume curves. Vagotomy was performed by sectioning the dorsal and ventral branches. To verify the action of GABAB receptors, baclofen was injected via icv (intracerebroventricular). Intravenous prazosin was used to produce chemical sympathectomy. The lesion in the PVN of the hypothalamus was performed using a 1mA/10s electrical current and GE was determined by measuring the percentage of gastric retention (% GR) of a saline meal. Results: No significant differences were observed regarding GC between groups; vagotomy significantly reduced % GR in INF group; icv treatment with baclofen significantly reduced %GR. GABAB receptors were not conclusively involved in delaying GE; intravenous treatment with prazosin significantly reduced GR% in INF group. PVN lesion abolished the effect of myocardial infarction on GE. Conclusion: Gastric emptying of liquids induced through acute myocardial infarction in rats showed the involvement of the vagus nerve, alpha1- adrenergic receptors and PVN.Fundamento: Distúrbios da motilidade do intestino proximal no infarto agudo do miocárdio podem desencadear sintomas digestivos como náuseas e vômitos. O infarto do miocárdio ocasiona retardo do esvaziamento gástrico (EG) de líquido em ratos. Objetivo: Investigar se existe a influência do nervo vago (VGX), adrenoreceptores α-1, receptores GABAB do sistema nervoso central e participação do núcleo paraventricular (NPV) do hipotálamo no esvaziamento gástrico (EG) e complacência gástrica (CG) em ratos infartados. Métodos: Ratos Wistar (n = 8-15) foram divididos em: grupo infarto (INF), sham (SH) e subdivididos. O infarto foi realizado por ligadura da artéria coronária descendente anterior. A complacência gástrica foi estimada com curvas pressão-volume. Realizada vagotomia por secção dos ramos dorsal e ventral. Para verificar a ação dos receptores GABAB foi injetado baclofeno por via intra ventrículo-cerebral. Simpatectomia química foi realizada com prazosina intravenosa (iv), e na lesão do núcleo paraventricular do hipotálamo foi utilizada corrente elétrica de 1mA/10s, com esvaziamento gástrico determinado por medição da retenção gástrica (% RG) de uma refeição salina. Resultados: Não houve diferença significativa na CG. A vagotomia (VGX) reduziu significativamente a %RG; no grupo INF, o tratamento intra ventrículo-cerebral (ivc) com baclofeno reduziu significativamente a % RG; não houve conclusivamente envolvimento dos receptores GABAB em retardar o EG; o tratamento intravenoso com prazosina reduziu significativamente a %RG no grupo INF. A lesão do NPV aboliu o efeito do infarto do miocárdio no EG. Conclusão: O nervo vago, receptores α-adrenérgicos e núcleo paraventricular estão envolvidos no retardo do esvaziamento gástrico no infarto agudo do miocárdio em ratos.

Enhanced D1 And D2 Inhibitions Induced By Low-frequency Trains Of Conditioning Stimuli: Differential Effects On H- And T-reflexes And Possible Mechanisms.

Mechanically evoked reflexes have been postulated to be less sensitive to presynaptic inhibition (PSI) than the H-reflex. This has implications on investigations of spinal cord neurophysiology that are based on the T-reflex. Preceding studies have shown an enhanced effect of PSI on the H-reflex when a train of ~10 conditioning stimuli at 1 Hz was applied to the nerve of the antagonist muscle. The main questions to be addressed in the present study are if indeed T-reflexes are less sensitive to PSI and whether (and to what extent and by what possible mechanisms) the effect of low frequency conditioning, found previously for the H-reflex, can be reproduced on T-reflexes from the soleus muscle. We explored two different conditioning-to-test (C-T) intervals: 15 and 100 ms (corresponding to D1 and D2 inhibitions, respectively). Test stimuli consisted of either electrical pulses applied to the posterior tibial nerve to elicit H-reflexes or mechanical percussion to the Achilles tendon to elicit T-reflexes. The 1 Hz train of conditioning electrical stimuli delivered to the common peroneal nerve induced a stronger effect of PSI as compared to a single conditioning pulse, for both reflexes (T and H), regardless of C-T-intervals. Moreover, the conditioning train of pulses (with respect to a single conditioning pulse) was proportionally more effective for T-reflexes as compared to H-reflexes (irrespective of the C-T interval), which might be associated with the differential contingent of Ia afferents activated by mechanical and electrical test stimuli. A conceivable explanation for the enhanced PSI effect in response to a train of stimuli is the occurrence of homosynaptic depression at synapses on inhibitory interneurons interposed within the PSI pathway. The present results add to the discussion of the sensitivity of the stretch reflex pathway to PSI and its functional role.

Cola beverage consumption delays alveolar bone healing: a histometric study in rats

Epidemiological studies have suggested that cola beverage consumption may affect bone metabolism and increase bone fracture risk. Experimental evidence linking cola beverage consumption to deleterious effects on bone is lacking. Herein, we investigated whether cola beverage consumption from weaning to early puberty delays the rate of reparative bone formation inside the socket of an extracted tooth in rats. Twenty male Wistar rats received cola beverage (cola group) or tap water (control group) ad libitum from the age of 23 days until tooth extraction at 42 days and euthanasia 2 and 3 weeks later. The neoformed bone volume inside the alveolar socket was estimated in semi-serial longitudinal sections using a quantitative differential point-counting method. Histological examination suggested a decrease in the osteogenic process within the tooth sockets of rats from both cola groups, which had thinner and sparser new bone trabeculae. Histometric data confirmed that alveolar bone healing was significantly delayed in cola-fed rats at three weeks after tooth extraction (ANOVA, p = 0.0006, followed by Tukey's test, p < 0.01). Although the results of studies in rats cannot be extrapolated directly to human clinical dentistry, the present study provides evidence that cola beverage consumption negatively affect maxillary bone formation.