The general differential-geometric structure of multidimensional Delsarte transmutation operators in parametric functional spaces and their applications in soliton theory. Part 2

The structure properties of multidimensional Delsarte transmutation operators in parametirc functional spaces are studied by means of differential-geometric tools. It is shown that kernels of the corresponding integral operator expressions depend on the topological structure of related homological cycles in the coordinate space. As a natural realization of the construction presented we build pairs of Lax type commutive differential operator expressions related via a Darboux-Backlund transformation having a lot of applications in solition theory. Some results are also sketched concerning theory of Delsarte transmutation operators for affine polynomial pencils of multidimensional differential operators.Comment: 10 page

The Hunter-Saxton equation: remarkable structures of symmetries and conserved densities

In this paper, we present extraordinary algebraic and geometrical structures for the Hunter-Saxton equation: infinitely many commuting and non-commuting $x,t$-independent higher order symmetries and conserved densities. Using a recursive relation, we explicitly generate infinitely many higher order conserved densities dependent on arbitrary parameters. We find three Nijenhuis recursion operators resulting from Hamiltonian pairs, of which two are new. They generate three hierarchies of commuting local symmetries. Finally, we give a local recursion operator depending on an arbitrary parameter. As a by-product, we classify all anti-symmetric operators of a definite form that are compatible with the Hamiltonian operator $D_x^{-1}$

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.Comment: 11 page

On a nonlocal Ostrovsky–Whitham type dynamical system, its Riemann type inhomogeneous regularizations and their integrability

Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm. The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The well defined regularization of the model is constructed and its Lax type integrability is discussed. A generalized hydrodynamical Riemann type system is considered, infinite hierarchies of conservation laws, related compatible Poisson structures and a Lax type representation for the special case N = 3 are constructed

What the Dynamic Systems Approach Can Offer for Understanding Development:An Example of Mid-childhood Reaching

The Dynamic Systems Approach (DSA) to development has been shown to be a promising theory to understand developmental changes. In this perspective, we use the example of mid-childhood (6- to 10-years of age) reaching to show how using the DSA can advance the understanding of development. Mid-childhood is an important developmental period that has often been overshadowed by the focus on the acquisition of reaching during infancy. This underrepresentation of mid-childhood studies is unjustified, as earlier studies showed that important developmental changes in mid-childhood reaching occur that refine the skill of reaching. We review these studies here for the first time and show that different studies revealed different developmental trends, such as non-monotonic and linear trends, for variables such as movement time and accuracy at target. Unfortunately, proposed explanations for these developmental changes have been tailored to individual studies, limiting their scope. Also, explanations were focused on a single component or process in the system that supposedly causes developmental changes. Here, we propose that the DSA can offer an overarching explanation for developmental changes in this research field. According to the DSA, motor behavior emerges from interactions of multiple components entailed by the person, environment, and task. Changes in all these components can potentially contribute to the emerging behavior. We show how the principles of change of the DSA can be used as an overarching framework by applying these principles not only to development, but also the behavior itself. This underlines its applicability to other fields of development

Cognitive disorders in patients with chronic kidney disease: Approaches to prevention and treatment

Background: Cognitive impairment is common in patients with chronic kidney disease (CKD), and early intervention may prevent the progression of this condition. Methods: Here, we review interventions for the complications of CKD (anemia, secondary hyperparathyroidism, metabolic acidosis, harmful effects of dialysis, the accumulation of uremic toxins) and for prevention of vascular events, interventions that may potentially be protective against cognitive impairment. Furthermore, we discuss nonpharmacological and pharmacological methods to prevent cognitive impairment and/or minimize the latter's impact on CKD patients' daily lives. Results: A particular attention on kidney function assessment is suggested during work-up for cognitive impairment. Different approaches are promising to reduce cognitive burden in patients with CKD but the availabe dedicated data are scarce. Conclusions: There is a need for studies assessing the effect of interventions on the cognitive function of patients with CKD

Porównanie wyników odchowu prosiąt otrzymujących różne preparaty żelaza

Comparison of the results of rearing the suckling piglets, receiving different Fe preparations. The aim of the studies was determine the results of rearing the piglets which received three different preparations of iron (Fe) by injection. The sows, the progeny of which was covered with the observations, were at random assigned before parturition, to one from three experimental groups – E1, E2 and E3 (5 sows in each group). The rate of growth, feed utilization and health state of the piglets from birth until weaning (35 day of life) was controlled. The highest body weight of 5-week old piglets was recorded in group E3; the difference in relation to body weight of the piglets from group E1 and 2 was equal to 3.47% and 13.15%, respectively (p>0.05). The best equalization of body weight of 5-week old piglets was found in groups E3 and E1. The piglets from group E3 consumed the greatest quantity of fixed feed until weaning; in the mentioned group, the body weight gain in total was the highest one (8.44 kg/head). The mean daily gains of the piglets from group E3 were equal to 241 g and they were higher as compared to group E1 and E2 by 5.24% and 12.62%, respectively. Consumption of solid feed per gain of 1kg of body weight of the litter amounted in groups E1, E2 and E3 to 4.80, 3.49 and 4.65 kg, respectively. The mentioned index was low what indicates a good milk performance of the sows. All three employed preparations fulfilled their prophylactic function and prevented incidence of anaemia symptoms.Porównanie wyników odchowu prosiąt otrzymujących różne preparaty żelaza. Celem badań było określenie wyników odchowu prosiąt otrzymujących iniekcyjnie trzy różne preparaty żelaza. Lochy których potomstwo objęto obserwacjami, przed porodem przydzielono losowo do jednej z trzech grup doświadczalnych - E1, E2 i E3 (każda po 5 loch). Kontrolowano tempo wzrostu, wykorzystanie paszy i stan zdrowia prosiąt od urodzenia do odsadzenia (35. dzień). Największą masę ciała 5. tygodniowych prosiąt stwierdzono w grupie E3; różnica w stosunku do masy prosiąt z grupy E1 i E2 wyniosła odpowiednio 3,47% i 13,15% (p>0,05). Najlepsze wyrównanie masy ciała 5. tygodniowych prosiąt stwierdzono w grupach E3 i E1. Prosięta z grupy E3 pobrały najwięcej paszy stałej do odsadzenia i w tej grupie przyrost masy ogółem był największy (8,44 kg/szt.). Średnie dobowe przyrosty prosiąt z grupy E3 wyniosły 241 g, i były większe vs grupy E1 i E2 o: 5,24% i 12,62%. Zużycie paszy stałej na przyrost 1 kg masy miotu wyniosło w grupach E1, E2, E3 odpowiednio: 4,80, 3,49 i 4,65 kg. Wskaźnik ten był niski co wskazuje na dobrą mleczność loch. Wszystkie trzy stosowane preparaty spełniły swoją profilaktyczną funkcję i zapobiegły wystąpieniu symptomów niedokrwistości

Quantum mathematics: backgrounds and some applications to nonlinear dynamical systems

Backgrounds of a new mathematical physics discipline ’Quantum Mathematics’ are discussed and analyzed from both historical and analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1934, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered.Обговорюються витоки нової дисциплiни в математичнiй фiзицi — квантової математики — як з iсторичної, так i з аналiтичної точок зору. Проiлюстровано дивовижнi властивостi методу вторинного квантування, який був запропонований Фоком у 1934 р., та розглянуто вражаючi застосування до теорiї нелiнiйних динамiчних систем