Discrete N-fold Darboux transformation and infinite number of conservation laws of a four-component Toda lattice

In this paper, we investigate a four-component Toda lattice (TL), which may be used to model the wave propagation in lattices just like the famous TL. By means of the Lax pair and gauge transformation, we construct the [Formula: see text]-fold Darboux transformation (DT), which enables us to obtain multi-soliton or multi-solitary wave solution without complex iterative process. Through the obtained DT, [Formula: see text]-fold explicit exact solutions of the system and their figures with proper parameters are presented from which we find the [Formula: see text]-fold solution shows two-solitary wave structure, the amplitude and shape of the wave change with time. Finally, we derive an infinite number of conservation laws formulaically to illustrate the integrability of the system.

Study of Ventricular Interdependence in Hemodialysis Patients

Background and objectivesStudy of respiratory variations in mitral valve (MV) Doppler flow in hemodialysis (HD) patients has not been investigated and normal adult referenced echocardiographic value is used as an echocardiographic reference to HD patients who have unique hemodynamic. This work aimed to study the respiratory variation in MV Doppler flow in HD patients to determine if it has a unique pattern in these patients, and to study any relation between this variation and volume-related parameters.MethodsWe conducted a prospective cohort study, carried out on 118 patients who underwent regular HD. A standard echocardiography was performed on the patients before and within 6 hs after dialysis. During quiet breathing, the transmitral spectral Doppler E wave was measured during inspiratory and expiratory phases using plethysmography breath-cycle chest-adhesive electrodes. The mathematic differences and the percent changes (ventricular interdependent; VI) in E wave were calculated pre-and post-dialysis. Post dialysis difference in the percent changes (∆ E wave % changes) was calculated as follows: pre-dialysis percent changes of E wave – post dialysis percent changes of E wave/pre dialysis percent changes E wave x 100. ResultsThe means of the mathematic differences between the MV inspiratory and expiratory E pre-and post-dialysis were 0.07 ± 0.18 m/s and 0.08 ± 0.22 m/s respectively with an insignificant difference between both phases; p = 0.337. Meanwhile, the means of the percent variation in the MV inspiratory and expiratory E pre-and post-dialysis were 56 ± 7 % and 44 ± 1.1 % respectively, with a significant reduction after dialysis; P = 0.000. Spearman correlation showed a significant positive correlation between post- dialysis ∆ E wave % change and post-dialysis % change of weight (r = 0.318; P = 0.000). Moreover, post- dialysis % change of weight and post- dialysis % changes of most other volume-related variable were independent predictors of post- dialysis ∆ E wave % in HD patients. ConclusionThe pre- and post- dialysis respiratory changes in the MV E wave in HD patients were higher than the normal adult referenced values. This marked variation could be explained by the unique overloading condition and could explain the LV diastolic dysfunction and the unexplained pulmonary hypertension in HD patients.

Risk Factors, Clinical Characteristics, and Prognosis of Acute Kidney Injury in Hospitalized COVID-19 Patients: A Retrospective Cohort Study

Background: Acute kidney injury (AKI) is a serious complication of COVID-19. Methods: Records of hospitalized adult patients with confirmed SARS-CoV-2 infection from 1 March to 31 May 2020 were retrospectively reviewed. Results: Of 283 patients, AKI occurred in 40.6%. From multivariate analyses, the risk factors of AKI in COVID-19 can be divided into: (1) demographics/co-morbidities (male, increasing age, diabetes, chronic kidney disease); (2) other organ involvements (transaminitis, elevated troponin I, ST segment/T wave change on electrocardiography); (3) elevated biomarkers (ferritin, lactate dehydrogenase); (4) possible bacterial co-infection (leukocytosis, elevated procalcitonin); (5) need for advanced oxygen delivery (non-invasive positive pressure ventilation, mechanical ventilation); and (6) other critical features (ICU admission, need for vasopressors, acute respiratory distress syndrome). Most AKIs were due to pre-renal (70.4%) and intrinsic (34.8%) causes. Renal replacement therapy was more common in intrinsic AKI. Both pre-renal (HR 3.2; 95% CI 1.7–5.9) and intrinsic AKI (HR 7.7; 95% CI 3.6–16.3) were associated with higher mortality. Male, stage 3 AKI, higher baseline and peak serum creatinine and blood urea nitrogen were prevalent in intrinsic AKI. Urine analysis and the fractional excretion of sodium and urea were not helpful in distinguishing intrinsic AKI from other causes. Conclusions: AKI is very common in COVID-19 and is associated with higher mortality. Characterization of AKI is warranted due to its diverse nature and clinical outcome.

Experimental Study on Directional Fracture Blasting of Cutting Seam Cartridge

Since the cutting seam cartridge has sound directional breaking effect, in order to explore its blasting wave mechanism, an experimental study was conducted on the blast wave of a cutting seam cartridge using a high-speed laser schlieren system and air overpressure test system. The research results show that during cartridge explosion, the cutting seam pipe can effectively control the energy release and detonation gas dynamic behaviors. Additionally, the cartridge blast wave and the detonation gas remain highly symmetrical in expansion form. The blast wave first propagates along the cutting seam direction, and the detonation gas initially expands from the seam in the direction of the cutting seam. The pressure in the cutting seam direction is higher than that in the noncutting seam direction. The blast wave change of the whole flow field of the cutting seam cartridge was numerically simulated and was basically consistent with the results of the schlieren test in distribution form. The presence of a cutting seam prolongs the blast wave effect. During expansion of the cutting seam pipe under the influence of a blast wave, the inner wall of the cutting seam pipe is mainly subject to tensile stress. When the tensile force applied to the inner wall reaches the local yield limit, the cutting seam pipe fails.

Solution to Propagation of Shock Wave Based on Continuum Hypothesis

Based on the continuum hypothesis, problem of compressing wave was studied analytically. By exploring the temperature distribution, the propagation velocity, and the thickness of the transition region, the developing process of compressing wave turning into shock wave was revealed, and the following conclusions were reached: (1) the governing equations of compressing wave can be turned into two autonomous equations, and the phase diagram can be used as an effective tool for the analysis of the compressing wave; (2) the solution of compressing wave was composed of two parts: the inner solution and the outer solution; when Pr=3/4, the analytical inner solution can be obtained; (3) as the disturbance velocity increases, the thickness of compressing wave will decrease, and the propagation velocity of the compressing wave will increase, and the compressing wave will become shock wave when the disturbance velocity is large enough; (4) velocity and temperature across compressing wave change monotonically and continuously, but the entropy generation changing tendency is closely related to Pr; therefore, the inner solution reveals the mechanism of irreversibility happening in compressing waves.