Embeddings between weighted Copson and Cesàro function spaces

In this paper, characterizations of the embeddings between weighted Copson function spaces \(Co{p_{{p_1},{q_1}}}\left( {{u_1},{v_1}} \right)\) and weighted Cesàro function spaces \(Ce{s_{{p_2},{q_2}}}\left( {{u_2},{v_2}} \right)\) are given. In particular, two-sided estimates of the optimal constant c in the inequality

$${\left( {\int_0^\infty {{{\left( {\int_0^t {f{{\left( \tau \right)}^{{p_2}}}{v_2}\left( \tau \right)d\tau } } \right)}^{{q_2}/{p_2}}}{u_2}\left( t \right)dt} } \right)^{1/{q_2}}} \leqslant c{\left( {\int_0^\infty {{{\left( {\int_t^\infty {f{{\left( \tau \right)}^{{p_1}}}{v_1}\left( \tau \right)d\tau } } \right)}^{{q_1}/{p_1}}}{u_1}\left( t \right)dt} } \right)^{1/{q_1}}},$$

where p₁, p₂, q₁, q₂ ∈ (0,∞), p₂ ≤ q₂ and u₁, u₂, v₁, v₂ are weights on (0,∞), are obtained. The most innovative part consists of the fact that possibly different parameters p₁ and p₂ and possibly different inner weights v₁ and v₂ are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesàro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities.

     

Natural convection in rectangular enclosures with partial heating and cooling

The flow and heat transfer in partially heated and partially cooled cavities were numerically analyzed. Using the control volume approach, a computer program based on SIMPLE algorithm was developed. A square enclosure with variable size heater and cooler on the vertical walls was considered. Computations were carried out to investigate the effects of heater and cooler size on the heat transfer rate. It was observed that for a given cooler size, the mean Nusselt number decreases with increasing heater size. On the other hand, for a given heater size, the mean Nusselt number increases with increasing cooler size. For all Rayleigh numbers considered, the same behavior was observed.

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Natürliche Konvektion in geschlossenen Räumen mit partieller Heizung und Kühlung der Wände

Zusammenfassung Es wurde ein numerisches Modell zur Analyse des Strömungs- und Wärmeübergangsverhaltens in teilweise beheizten und gekühlten Hohlräumen entwickelt und unter Verwendung des Kontrollvolumenprinzips und des Algorithmus SIMPLE als Computer-Programm formuliert. Der Hohlraum ist rechteckig und die variablen Heiz- und Kühlflächen befinden sich auf gegenüberliegenden Vertikalseiten. Hauptziel der Berechnungen war es, den Einfluß der variablen Heiz- und Kühlflächen auf den Wärmeübergang zu ermitteln. Für eine bestimmte Kühlergröße zeigte sich eine Abnahme der gemittelten Nußelt-Zahl mit zunehmender Heizfläche. Andererseits — bei gegebener Heizfläche — stieg die Nußelt-Zahl mit der Kühlfläche an. Dieses Verhalten wurde bei allen untersuchten Rayleighzahlen gefunden.

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Nomenclature g gravitational acceleration - H height of cavity - k thermal conductivity of fluid - l _C cooler size - l _H heater size - mean Nusselt number - Nu _y local Nusselt number - P pressure - Pr Prandtl number - Ra Rayleigh number (Ra = gH ³(T _H –T _C)/()) - T temperature - T _C temperature of cold surface - T _H temperature of hot surface - T _R reference temperature (T _R = (T _C +T _H)/2) - u velocity component inx-direction - x horizontal axis - v velocity component iny-direction - y vertical axis Greek symbols thermal diffusivity - thermal expansion coefficient - density of fluid - stream function - kinematic viscosity     

Heat transfer in an oscillating vertical annular liquid column open to atmosphere

The heat transfer from a surface heated with constant heat flux to an oscillating vertical annular liquid column having an interface with the atmosphere is investigated experimentally in the present paper. The analysis is carried out for the case of different oscillation frequencies while the displacement amplitude remains constant. Based on the experimental data a correlation equation is obtained for the cycle-averaged Nusselt number as a function of kinetic Reynolds number.     

On the dynamic snap-out instability of inflated non-linear spherical membranes

The dynamic behavior of a spherical membrane, made of Mooney material and subjected to a uniform inflating step-pressure, is studied. Its phase-planes and nondimensional radius versus time curves are plotted for different values of the material constants. The conditions for dynamic snapout instability are discussed. The relations between the static behavior of the membrane and the dynamic instability are pointed out.     

A new agent for sentinel lymph node detection: preliminary results

Sentinel lymph node detection is widely used to identify lymph nodes that receive lymphatic drainage from a primary tumor. ^99mTc labeled iron oxide nanoparticles were prepared to invent a new colorful radioactive agent for sentinel lymph node detection. Iron oxide nanoparticles were produced by co-precipitation of FeCl₃ and FeCl₂ in the presence of NaOH. Then iron oxide nanoparticles were labeled with ^99mTc. ^99mTc labeled nanoparticles (7.4 MBq/0.1 mL) were intradermally injected in the distal hind limb of 16 rabbits. Dynamic and static lymphoscintigraphic images were taken for 24 h. Labeling efficiencies of ^99mTc-iron oxide nanoparticles were over 99%. Their sizes are between 50 and 60 nm. ^99mTc-iron oxide nanoparticles were accumulated in the popliteal lymph node in 11 of 16 rabbits (69%). Retention of nanoparticles in the popliteal lymph node was obvious at from 2nd through 24th hours. The radioactive lymph node was identified easily by gamma probe. The popliteal lymph node was excised and established for radioactivity and black dye. These black and radioactive nanoparticles may be potential agent successfully used for sentinel lymph node detection.     

Microcalorimetric investigation of water vapor adsorption on silica gel

In this study, the activities of four ginsenosides Rc, Re, Rd, and Rf on splenic lymphocytes growth were studied by microcalorimetry. Some qualitative and quantitative information, such as the metabolic power–time curves, growth rate constant k, maximum heat-output power of the exponential phase P _max and the corresponding appearance peak time t _max, total heat output Q _t, and promotion rate R _p of splenic lymphocytes growth affected by the four ginsenosides were calculated. In accordance with thermo-kinetic model, the corresponding quantitative relationships of k, P _max, t _max, Q _t, R _p, and c were established, . Also, the median effective concentration (EC₅₀) was obtained by quantitative analysis. Based on both the quantitative quantity–activity relationships (QQAR) and EC₅₀, the sequence of promotion activity was Rc > Re > Rd > Rf. The analysis of structure–activity relationships showed that the number, type, and position of sugar moieties on the gonane steroid nucleus had important influences on the promotion activity of Rc, Re, Rd, and Rf on splenic lymphocytes growth. Microcalorimetry can be used as a useful tool for determining the activity and studying the quantity–activity relationship of drugs on cell.     

Operator splitting for numerical solution of the modified Burgers' equation using finite element method

The aim of this study is to obtain numerical behavior of a one‐dimensional modified Burgers' equation using cubic B‐spline collocation finite element method after splitting the equation with Strang splitting technique. Moreover, the Ext4 and Ext6 methods based on Strang splitting and derived from extrapolation have also been applied to the equation. To observe how good and effective this technique is, we have used the well‐known the error norms L₂ and L_∞ in the literature and compared them with previous studies. In addition, the von Neumann (Fourier series) method has been applied after the nonlinear term has been linearized to investigate the stability of the method.     

Kernel of the classicalZitterbewegung

Barut's classicalzitterbewegung model includes the internal dynamical variables and the quantization of this system gives a general transition amplitude between the different space-time points and internal coordinates and momentum. It includes the transition amplitude between the half integer and integer spin eigenvalues. Spin eigenfunctions lead to all sets of relativistic wave equations, as well as the Dirac equation.     

Contribution of electrolyte pH and deposition potentials to the magnetic anisotropy of electrodeposited nickel films

The influence of electrolyte pH and cathode potential on the magnetic properties of single layer Nickel films electrodeposited on polycrystalline titanium substrates was studied. The films were deposited at the electrolyte pH=3.5±0.1, 2.5±0.1 and 2.1±0.1 by varying the deposition potentials (?1.2, ?1.5 and ?1.8 V vs saturated calomel electrode, SCE) applied in continuous waveform. The structural analysis by X-ray diffraction revealed that the films have face-centred cubic structure. Results of the magnetic measurements obtained by vibrating sample magnetometer (VSM) indicated that the magnetic properties were affected by the electrolyte pH and the cathode potentials in terms of magnetic anisotropy. At the highest pH the films deposited at the lowest potential had in-plane magnetic anisotropy. As the electrolyte pH decreased from the high (pH=3.5±0.1) to low (pH=2.5±0.1), which is aided by increasing the potentials, resulted in an almost magnetic isotropy in the films. However, isotropic magnetic behaviour was observed for the film deposited at the low pH combined with the high potential (?1.8 V vs SCE). Magnetic thickness profile of the samples obtained by VSM revealed that the isotropic films have a smoother magnetic variation across the film from one edge than the anisotropic ones. This is also verified with a microscopic observation by an optical microscope and the surface of the isotropic films is observed to be smoother than that of the anisotropic ones. Furthermore, all films were found to have planar magnetic anisotropy irrespective of the pH’s and the potentials.