Academic literature on the topic 'K-inner Functions'

Inner functions inQK(p,q)are studied, providedKsatisfies certain regularity conditions. In particular, it is shown that the only inner functions inQK(p, p-2), p≥1, are precisely the Blaschke products whose zeros{zn}satisfysup⁡a∈D∑K(1-|φa(zn)|2)<∞.

AbstractIt is shown that given any sequence of automorphisms (ϕk)k of the unit ball of ℂN such that ‖ϕk(0)‖ tends to 1, there exists an inner function I such that the family of “non-Euclidean translates” (I о ϕk)k is locally uniformly dense in the unit ball of H∞().

Abstract In this paper, under some conditions on weighted function K, we give some new equivalent characterizations of inner functions in Q K spaces. Meanwhile, we also studied inner functions in Q K spaces as multipliers of C 𝓑(Q K ) ∩ BMOA, where C 𝓑(Q K ) denoted the closure of Q K spaces in Bloch spaces.

The Berezin symbol ?A of an operator A on the reproducing kernel Hilbert space H (?) over some set ? with the reproducing kernel k? is defined by ? (?) = ?A k?/||k?||, k?/||k?||?, ? ? ?. The Berezin number of an operator A is defined by ber(A) := sup ??? |?(?)|. We study some problems of operator theory by using this bounded function ?, including treatments of inner product inequalities via convex functions for the Berezin numbers of some operators. We also establish some inequalities involving of the Berezin inequalities.

Let $\{\varphi_{k}\}_{k=0}^\infty$ be a system of functions defined on $ [a, b] $ and orthonormal in $ L ^ 2_ \rho = L ^ 2_\rho ( a, b) $ with respect to the usual inner product. For a given positive integer $ r $, by $\{\varphi_{r,k}\}_{k=0}^\infty$ we denote the system of functions orthonormal with respect to the Sobolev-type inner product and generated by the system $\{\varphi_{k}\}_{k=0}^\infty$. In this paper, we study the question of the uniform convergence of the Fourier series by the system of functions $\{\varphi_{r,k}\}_{k=0}^\infty$ to the functions $f\in W^r_{L^p_\rho}$ in the case when the original system $\{\varphi_{k}\}_{k=0}^\infty$ forms a basis in the space $L^p_\rho=L^p_\rho(a,b)$ ($1\le p$, $p\neq2$).

Abstract The present paper introduces and studies the concepts of K-outer approximation and K-inner approximation for a monotone function μ defined on a D-poset P, by a subfamily K of P. Some desirable properties of K-approximable functions are established and it is shown that the family of all elements of P that possess K-approximation, forms a lattice and is closed under orthosupplementation. We have proved that a submodular measure on a suitable subfamily of P having K-outer approximation can be extended to a function that has K-outer approximation, and a tight function that has K-inner approximation can be extended to a function having K-inner approximation.

In this paper we consider the system of functions G_(r,n)^α (x) (r∈N,n=0,1,…) which is orthogonal with respect to the Sobolev-type inner product on (-1,1) and generated by orthogonal Gegenbauer polynomials. The main goal of this work is to study some properties related to the system {φ_(k,r) (x)}_(k≥0) of the functions generated by the orthogonal system {G_(r,n)^α (x)} of Gegenbauer functions. We study the conditions on a function f(x) given in a generalized Gegenbauer orthogonal system for it to be expandable into a generalized mixed Fourier series of the form f(x)~∑_(k=0)^(r-1)▒〖f^((k) ) (-1) (x+1)^k/k!+∑_(k=r)^∞▒〖G_(r,k)^α (f) 〗〗 φ_(r,k)^α (x), as well as the convergence of this Fourier series. The second result of this paper is the proof of a recurrence formula for the system {φ_(k,r) (x)}_(k≥0). We also discuss the asymptotic properties of these functions, and this represents the latter result of our contribution.

The purpose of this paper is to prove functional equations of L-functions associated with the vector space of binary quadratic forms and determine their poles and residues. For a commutative ring K, let V(K) be the set of all symmetric matrices of degree 2 with coefficients in K. In V(C), we consider the inner productwhere for .

A GABA- or glycine-induced increase in Cl− permeability can produce either a depolarization or hyperpolarization, depending on the Cl− equilibrium potential. It has been shown that retinal neurons express the chloride cotransporters, Na-K-2Cl (NKCC) and K-Cl (KCC), the primary molecular mechanisms that control the intracellular Cl− concentration. We thus studied (1) the localization of these cotransporters in the fish retina, and (2) how suppression of cotransporter activity in the fish retina affects function. Specific antibodies against NKCC and KCC2 revealed that both cotransporters were expressed in the outer and inner plexiform layers, and colocalized in many putative amacrine cells and in cells of the ganglion cell layer. However, the somata of putative horizontal cells displayed only NKCC immunoreactivity and many bipolar cells were only immunopositive for KCC2. In the outer retina, application of bumetanide, a specific inhibitor of NKCC activity, (1) increased the steady-state extracellular concentration of K+ ([K+]o) and enhanced the light-induced decrease in the [K+]o, (2) increased the sPIII photoreceptor-dependent component of the ERG, and (3) reduced the extracellular space volume. In contrast, in the outer retina, application of furosemide, a specific inhibitor of KCC activity, decreased sPIII and the light-induced reduction in [K+]o, but had little effect on steady-state [K+]o. In the inner retina, bumetanide increased the sustained component of the light-induced increase in [K+]o. These findings thus indicate that NKCC and KCC2 control the [K+]o and extracellular space volume in the retina in addition to regulating GABA- and glycine-mediated synaptic transmission. In addition, the anatomical and electrophysiological results together suggest that all of the major neuronal types in the fish retina are influenced by chloride cotransporter activity.

This thesis concerns dilation theory, analytic models, joint invariant subspaces, reproducing kernelHilbert spaces and multipliers associated to commuting tuples of bounded linear operators on Hilbert spaces. The main contribution of this thesis is twofold: dilation and analytic model theory for n-tuples of (1) commuting contractions (in the setting of the unit polydisc), and (2) commuting row contractions (in the setting of the unit ball). On n-tuples of commuting contractions: We study analytic models of operators with some positivity assumptions and quotient modules of function Hilbert spaces over polydisc. We prove that for an m-hypercontraction T 2 C¢0 on a Hilbert space H, there exist Hilbert spaces E and E¤, and a partially isometric multiplier µ 2M ¡H2 E (D), A2 m(E¤) ¢ such that H » Æ Qµ Æ A2 m(E¤)ªµH2 E (D), and T » Æ PQµMz jQµ , where A2 m(E¤) is the E¤-valued weighted Bergman space and H2 E (D) is the E -valued Hardy space over the unit disc D. We then proceed to study and develop analytic models for doubly commuting n-tuples of operators and investigate their applications to joint shift co-invariant subspaces of reproducing kernel Hilbert spaces over polydisc. In particular, we completely analyze doubly commuting quotient modules of a large class of reproducing kernel Hilbert modules, in the sense of Arazy and Englis, over the unit polydisc Dn. On commuting row contractions: We study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. We prove that for a large class of analytic functional Hilbert spaces HK on the unit ball in Cn, wandering subspaces for restrictions of the multiplication tupleMz Æ (Mz1 , . . . ,Mzn ) can be described in terms of suitable HK -inner functions. We prove that, HK -inner functions are contractive multipliers and deduce a result on the multiplier norm of quasi-homogenous polynomials as an application. Along the way we prove a refinement of a result of Arveson on the uniqueness of minimal dilations of pure row contractions.

Bones are multifunctional passive organs of movement that supports soft tissue and directly attached muscles. They also protect internal organs and are a reserve of calcium, phosphorus and magnesium. Each bone is covered with periosteum, and the adjacent bone surfaces are covered by articular cartilage. Histologically, the bone is an organ composed of many different tissues. The main component is bone tissue (cortical and spongy) composed of a set of bone cells and intercellular substance (mineral and organic), it also contains fat, hematopoietic (bone marrow) and cartilaginous tissue. Bones are a tissue that even in adult life retains the ability to change shape and structure depending on changes in their mechanical and hormonal environment, as well as self-renewal and repair capabilities. This process is called bone turnover. The basic processes of bone turnover are: • bone modeling (incessantly changes in bone shape during individual growth) following resorption and tissue formation at various locations (e.g. bone marrow formation) to increase mass and skeletal morphology. This process occurs in the bones of growing individuals and stops after reaching puberty • bone remodeling (processes involve in maintaining bone tissue by resorbing and replacing old bone tissue with new tissue in the same place, e.g. repairing micro fractures). It is a process involving the removal and internal remodeling of existing bone and is responsible for maintaining tissue mass and architecture of mature bones. Bone turnover is regulated by two types of transformation: • osteoclastogenesis, i.e. formation of cells responsible for bone resorption • osteoblastogenesis, i.e. formation of cells responsible for bone formation (bone matrix synthesis and mineralization) Bone maturity can be defined as the completion of basic structural development and mineralization leading to maximum mass and optimal mechanical strength. The highest rate of increase in pig bone mass is observed in the first twelve weeks after birth. This period of growth is considered crucial for optimizing the growth of the skeleton of pigs, because the degree of bone mineralization in later life stages (adulthood) depends largely on the amount of bone minerals accumulated in the early stages of their growth. The development of the technique allows to determine the condition of the skeletal system (or individual bones) in living animals by methods used in human medicine, or after their slaughter. For in vivo determination of bone properties, Abstract 10 double energy X-ray absorptiometry or computed tomography scanning techniques are used. Both methods allow the quantification of mineral content and bone mineral density. The most important property from a practical point of view is the bone’s bending strength, which is directly determined by the maximum bending force. The most important factors affecting bone strength are: • age (growth period), • gender and the associated hormonal balance, • genotype and modification of genes responsible for bone growth • chemical composition of the body (protein and fat content, and the proportion between these components), • physical activity and related bone load, • nutritional factors: – protein intake influencing synthesis of organic matrix of bone, – content of minerals in the feed (CA, P, Zn, Ca/P, Mg, Mn, Na, Cl, K, Cu ratio) influencing synthesis of the inorganic matrix of bone, – mineral/protein ratio in the diet (Ca/protein, P/protein, Zn/protein) – feed energy concentration, – energy source (content of saturated fatty acids - SFA, content of polyun saturated fatty acids - PUFA, in particular ALA, EPA, DPA, DHA), – feed additives, in particular: enzymes (e.g. phytase releasing of minerals bounded in phytin complexes), probiotics and prebiotics (e.g. inulin improving the function of the digestive tract by increasing absorption of nutrients), – vitamin content that regulate metabolism and biochemical changes occurring in bone tissue (e.g. vitamin D3, B6, C and K). This study was based on the results of research experiments from available literature, and studies on growing pigs carried out at the Kielanowski Institute of Animal Physiology and Nutrition, Polish Academy of Sciences. The tests were performed in total on 300 pigs of Duroc, Pietrain, Puławska breeds, line 990 and hybrids (Great White × Duroc, Great White × Landrace), PIC pigs, slaughtered at different body weight during the growth period from 15 to 130 kg. Bones for biomechanical tests were collected after slaughter from each pig. Their length, mass and volume were determined. Based on these measurements, the specific weight (density, g/cm3) was calculated. Then each bone was cut in the middle of the shaft and the outer and inner diameters were measured both horizontally and vertically. Based on these measurements, the following indicators were calculated: • cortical thickness, • cortical surface, • cortical index. Abstract 11 Bone strength was tested by a three-point bending test. The obtained data enabled the determination of: • bending force (the magnitude of the maximum force at which disintegration and disruption of bone structure occurs), • strength (the amount of maximum force needed to break/crack of bone), • stiffness (quotient of the force acting on the bone and the amount of displacement occurring under the influence of this force). Investigation of changes in physical and biomechanical features of bones during growth was performed on pigs of the synthetic 990 line growing from 15 to 130 kg body weight. The animals were slaughtered successively at a body weight of 15, 30, 40, 50, 70, 90, 110 and 130 kg. After slaughter, the following bones were separated from the right half-carcass: humerus, 3rd and 4th metatarsal bone, femur, tibia and fibula as well as 3rd and 4th metatarsal bone. The features of bones were determined using methods described in the methodology. Describing bone growth with the Gompertz equation, it was found that the earliest slowdown of bone growth curve was observed for metacarpal and metatarsal bones. This means that these bones matured the most quickly. The established data also indicate that the rib is the slowest maturing bone. The femur, humerus, tibia and fibula were between the values of these features for the metatarsal, metacarpal and rib bones. The rate of increase in bone mass and length differed significantly between the examined bones, but in all cases it was lower (coefficient b <1) than the growth rate of the whole body of the animal. The fastest growth rate was estimated for the rib mass (coefficient b = 0.93). Among the long bones, the humerus (coefficient b = 0.81) was characterized by the fastest rate of weight gain, however femur the smallest (coefficient b = 0.71). The lowest rate of bone mass increase was observed in the foot bones, with the metacarpal bones having a slightly higher value of coefficient b than the metatarsal bones (0.67 vs 0.62). The third bone had a lower growth rate than the fourth bone, regardless of whether they were metatarsal or metacarpal. The value of the bending force increased as the animals grew. Regardless of the growth point tested, the highest values were observed for the humerus, tibia and femur, smaller for the metatarsal and metacarpal bone, and the lowest for the fibula and rib. The rate of change in the value of this indicator increased at a similar rate as the body weight changes of the animals in the case of the fibula and the fourth metacarpal bone (b value = 0.98), and more slowly in the case of the metatarsal bone, the third metacarpal bone, and the tibia bone (values of the b ratio 0.81–0.85), and the slowest femur, humerus and rib (value of b = 0.60–0.66). Bone stiffness increased as animals grew. Regardless of the growth point tested, the highest values were observed for the humerus, tibia and femur, smaller for the metatarsal and metacarpal bone, and the lowest for the fibula and rib. Abstract 12 The rate of change in the value of this indicator changed at a faster rate than the increase in weight of pigs in the case of metacarpal and metatarsal bones (coefficient b = 1.01–1.22), slightly slower in the case of fibula (coefficient b = 0.92), definitely slower in the case of the tibia (b = 0.73), ribs (b = 0.66), femur (b = 0.59) and humerus (b = 0.50). Bone strength increased as animals grew. Regardless of the growth point tested, bone strength was as follows femur > tibia > humerus > 4 metacarpal> 3 metacarpal> 3 metatarsal > 4 metatarsal > rib> fibula. The rate of increase in strength of all examined bones was greater than the rate of weight gain of pigs (value of the coefficient b = 2.04–3.26). As the animals grew, the bone density increased. However, the growth rate of this indicator for the majority of bones was slower than the rate of weight gain (the value of the coefficient b ranged from 0.37 – humerus to 0.84 – fibula). The exception was the rib, whose density increased at a similar pace increasing the body weight of animals (value of the coefficient b = 0.97). The study on the influence of the breed and the feeding intensity on bone characteristics (physical and biomechanical) was performed on pigs of the breeds Duroc, Pietrain, and synthetic 990 during a growth period of 15 to 70 kg body weight. Animals were fed ad libitum or dosed system. After slaughter at a body weight of 70 kg, three bones were taken from the right half-carcass: femur, three metatarsal, and three metacarpal and subjected to the determinations described in the methodology. The weight of bones of animals fed aa libitum was significantly lower than in pigs fed restrictively All bones of Duroc breed were significantly heavier and longer than Pietrain and 990 pig bones. The average values of bending force for the examined bones took the following order: III metatarsal bone (63.5 kg) <III metacarpal bone (77.9 kg) <femur (271.5 kg). The feeding system and breed of pigs had no significant effect on the value of this indicator. The average values of the bones strength took the following order: III metatarsal bone (92.6 kg) <III metacarpal (107.2 kg) <femur (353.1 kg). Feeding intensity and breed of animals had no significant effect on the value of this feature of the bones tested. The average bone density took the following order: femur (1.23 g/cm3) <III metatarsal bone (1.26 g/cm3) <III metacarpal bone (1.34 g / cm3). The density of bones of animals fed aa libitum was higher (P<0.01) than in animals fed with a dosing system. The density of examined bones within the breeds took the following order: Pietrain race> line 990> Duroc race. The differences between the “extreme” breeds were: 7.2% (III metatarsal bone), 8.3% (III metacarpal bone), 8.4% (femur). Abstract 13 The average bone stiffness took the following order: III metatarsal bone (35.1 kg/mm) <III metacarpus (41.5 kg/mm) <femur (60.5 kg/mm). This indicator did not differ between the groups of pigs fed at different intensity, except for the metacarpal bone, which was more stiffer in pigs fed aa libitum (P<0.05). The femur of animals fed ad libitum showed a tendency (P<0.09) to be more stiffer and a force of 4.5 kg required for its displacement by 1 mm. Breed differences in stiffness were found for the femur (P <0.05) and III metacarpal bone (P <0.05). For femur, the highest value of this indicator was found in Pietrain pigs (64.5 kg/mm), lower in pigs of 990 line (61.6 kg/mm) and the lowest in Duroc pigs (55.3 kg/mm). In turn, the 3rd metacarpal bone of Duroc and Pietrain pigs had similar stiffness (39.0 and 40.0 kg/mm respectively) and was smaller than that of line 990 pigs (45.4 kg/mm). The thickness of the cortical bone layer took the following order: III metatarsal bone (2.25 mm) <III metacarpal bone (2.41 mm) <femur (5.12 mm). The feeding system did not affect this indicator. Breed differences (P <0.05) for this trait were found only for the femur bone: Duroc (5.42 mm)> line 990 (5.13 mm)> Pietrain (4.81 mm). The cross sectional area of the examined bones was arranged in the following order: III metatarsal bone (84 mm2) <III metacarpal bone (90 mm2) <femur (286 mm2). The feeding system had no effect on the value of this bone trait, with the exception of the femur, which in animals fed the dosing system was 4.7% higher (P<0.05) than in pigs fed ad libitum. Breed differences (P<0.01) in the coross sectional area were found only in femur and III metatarsal bone. The value of this indicator was the highest in Duroc pigs, lower in 990 animals and the lowest in Pietrain pigs. The cortical index of individual bones was in the following order: III metatarsal bone (31.86) <III metacarpal bone (33.86) <femur (44.75). However, its value did not significantly depend on the intensity of feeding or the breed of pigs.

Ship parametric roll is one of the main reasons for marine accidents and is introduced into the second-generation intact stability criteria by the International Maritime Organization (IMO) recently. In this paper, a 6-DOF three-dimensional time-domain model based on the IRF (Impulse Response Function) method is constructed to predict large-amplitude ship motions and investigate the phenomenon of parametric roll in head waves as well as major factors. The F-K forces and the restoring forces are calculated on the instantaneous wet surface while the radiation and diffraction forces are kept linear and transformed from frequency-domain results calculated with the three-dimensional Havelock form translating-pulsating source green function method. The proposed weakly nonlinear time-domain model is used to simulate motions of the C11 containership, which predicts the occurrence of the parametric roll successfully and shows a good agreement with the experimental data in amplitude. The inner mechanism of parametric roll is revealed by investigating the time-history and resonance frequencies of restoring forces and coefficients numerically.

We now consider how the military base area operated, as a zone where a large number of people lived and worked on a routine basis. On one hand, to function it required the affordances of its internal communications, connections with the civil town, and access to roads, river, and lands beyond the walls; on the other, there was a need for surveillance and control of activities within the base, and of movements across its boundary. The most obvious part of the base boundary (Plate XXII) is the substantial mud brick wall ploughed across four blocks from the city defences just S of Tower 21, and blocking Wall, A, C, and D Sts, with a gate established at B St. How the S boundary was defined E of D St has always remained an issue. If it was necessary to build a wall at the W end, why was this not simply continued all the way to, e.g., the S end of the Citadel? Across blocks F7 and F5 it seems that the boundary of the military zone simply comprised party walls between military and civilian-occupied structures. The same was true within block B2, by the Citadel, although the boundary probably comprised building frontages along Lower Main St. On the plateau, as the camp wall may have been a subsequent local enhancement, except where the amphitheatre formed part of it, the boundary may generally have comprised the rear walls of military-held houses lining the S side of 8th St—probably all properties from the city wall to H St. The course of the boundary along the W side of the inner wadi is unknown, but the base is suggested, as along 8th St, to have incorporated at least all properties lining the S side of the Wadi Ascent Road, if not encompassing all blocks on the wadi slope—in which case the boundary here may rather have comprised property frontages on K St. The base area was split by site topography into two major zones, the flat plateau, and the N branch of the inner wadi around the Citadel. Each was further subdivided.

One of the most common subjects of world painting is associated with images of a woman with a book. The article uses the example of 32 canvases from the middle of the 18th – first half of the 19th century. The issue of functions of a book as an element of a female portrait is considered. The space depicted in these paintings can be chamber-limited or completely open, subject-ascetic or materially saturated. However, the article is mainly focused on the space of women’s life and a book as its marker. Under the brush of the artist, the book turns out to be an indicator of a woman’s living space: in some cases it highlights the social significance of her activities (portraits of Catherine II, Princess E.R. Dashkova, poetess A.P. Bunina), in others it shows the content of everyday leisure (portraits of Marquise de Pompadour, Grand Duchess Maria Alexandrovna, etc.), finally, with the help of a book, the mental state of the heroine is characterized, in other words, the space of her inner world is depicted (portraits of V. Monacharova, E.A. Demidova, etc.).

Innumerable experiments have been performed on both inner- and outer-sphere electron-transfer reactions. We do not review them here, but present a few results that are directly relevant to the theoretical issues raised in the preceding chapters. The Butler-Volmer equation (5.10) predicts that for |η| > kT/e0 a plot of the logarithm of the current versus the applied potential (Tafel plot) should result in a straight line, whose slope is determined by the transfer coefficient α. Because of the dual role of the transfer coefficient (see Section 5.2), it is important to verify that the transfer coefficient obtained from a Tafel plot is independent of temperature. We shall see later that proton- and ion-transfer reactions often give straight lines in Tafel plots, too, but the apparent transfer coefficient obtained from these plots can depend on the temperature, indicating that these reactions do not obey the Butler-Volmer law. In order to test the temperature independence of the transfer coefficient, Curtiss et al. investigated the kinetics of the Fe2+/Fe3+ reaction on gold in a pressurized aqueous solution of perchloric acid over a temperature range from 25° to 75°C. In the absence of trace impurities of chloride ions, this reaction proceeds via an outer sphere mechanism with a low rate constant (k0 ≈ 10-5 cm s-1 at room temperature). Figure 8.1 shows the slope of their Tafel plots, d(lni)/dη, as a function of the inverse temperature 1/T. The Butler-Volmer equation predicts a straight line of slope αe0/k, which is indeed observed. Over the investigated temperature range both the transfer coefficient and the energy of activation are constant: α = 0.425 ± 0.01 and Eact = 0.59± 0.01 eV at equilibrium, confirming the validity of the Butler-Volmer equation in the region of low overpotentials, from which the Tafel slopes were obtained. The phenomenological derivation of the Butler-Volmer equation is based on a linear expansion of the Gibbs energy of activation with respect to the applied overpotential. At large overpotentials higher-order terms are expected to contribute, and a Tafel plot should no longer be linear.

The b-wave of the ERG has been used as a measure of the activity of the inner nuclear layer. Fulton and Rushton1 recorded human ERGs elicited by flashes of different intensities and fitted their data with the function where R is the trough-to-peak amplitude of the b-wave, Rm is the maximum amplitude, I is the flash intensity, and K is the semisaturation intensity. They observed that light adaptation changed the values of K and Rm and associated these changes with modification in "the b-wave generating mechanism". Arden et al2 extended this analysis to retinal disease by measuring response-intensity functions in patients and relating changes in K and Rm to the action of a disease at the receptors and/or "the b-wave generating mechanism". Since this study, hundreds of response-intensity functions have been collected in the clinic and the parameters K and Rm estimated.3−9 The solid curves in Fig. 1A show three ERG responses from a typical response-intensity series.7 The filled circles in Fig. 1B show the trough-to-peak b-wave amplitudes for the complete data set. The solid curve in Fig. 1B is the best fit of eq. 1 to the b-wave amplitudes.

Central retinal vein occlusion (CRVO) is a disorder in which the circulation to the inner retina is impaired because of a blockage of the central retinal vein. The occlusion can produce severe inner retinal ischemia, leading in some patients to the blinding complication of neovascular glaucoma. In these patients, the choroidal circulation, which serves the photoreceptors, is not impaired. Several types of changes are seen in the electroretinogram (ERG) of patients with CRVO. Sabates and his associates1 have reported preferential reductions in the b-wave amplitude relative to the a-wave amplitude in CRVO eyes that develop iris neovascularization. Johnson and co-workers2 have measured ERG intensity-response functions in patients with CRVO and have analyzed the b-wave amplitudes by fitting the data with the Naka-Rushton function: (1) where I and R are intensity, response ordered pairs, Rmax is the maximum b-wave amplitude (measured from the trough of the a-wave to the peak of the b-wave), K is the half-saturation constant (because when I = K, R = 1/2 Rmax) and n is the slope. In normal observers, these parameters vary independently.3

This paper deals with CFD predictions for flow and heat transfer in supercritical water in a bare tube. Studies were performed using the software FLUENT for upward flows in vertical tubes with heated length of 4 m and an inner diameter of 10 mm at high values of mass flux (G > 1000 kg/m2s). Turbulence models verification data for the given physical conditions are presented. Besides the testing of different turbulence models that are presented in modern catalog of these models is carried out. Namely, the models related to the following three groups: High–Reynolds number k-ε models with wall functions, k-ω models and Low-Reynolds number k-ε models were considered. On the basis of performed studies the best compliance of known experimental data with computer simulation results fits the k-ω SST turbulence model is shown.

The horizontal frame members that often protrude from the inner surface of a window can significantly effect the convective heat transfer rate from this inner surface to the room. The purpose of the present numerical study was to determine how the size of a pair of horizontal frame members effect this heat transfer rate. The flow has been assumed to be steady and conditions under which laminar, transitional, and turbulent flows occur are considered. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being dealt with using the Boussinesq approach. The governing equations have been solved using the FLUENT commercial CFD code. The k-epsilon turbulence model with standard wall functions and with buoyancy force effects fully accounted for has been used. The solution has the following parameters: the Rayleigh number, the Prandtl number, the dimensionless window recess depth, and the dimensionless width and depth of the frame members. Results have been obtained for a Prandtl number of 0.74.

The vertical and horizontal frame members that often protrude from the inner surface of a window can, in some situations, have a significant effect on the convective heat transfer rate from the inner (room-side) surface of the window to the room. The purpose of the present numerical study was to determine, in a basic way, how the relative size of a single horizontal frame member mounted in the center of the window affects this convective heat transfer rate. A recessed window has been considered. The flow has been assumed to be steady and both laminar and turbulent flows have been considered. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being dealt with using the Boussinesq approach. The governing equations have been solved using the FLUENT commercial cfd code. The k-epsilon turbulence model with standard wall functions and with buoyancy force effects fully accounted for has been used in the calculations. The solution has the following parameters: the Rayleigh number, the Prandtl number, the dimensionless horizontal distance between the inner window surface and the inner surface of the wall in which the window is mounted (the dimensionless recess depth), and the dimensionless width and depth of the frame member. Results have only been obtained for a Prandtl number of 0.74, which is effectively the value for air, and for single values of the dimensionless window recess depth and of the dimensionless frame height. The effects of the other dimensionless variables on the window Nusselt number have been numerically studied.

To improve the gas turbine thermal performance, apart from using a high compression ratio, the turbine inlet temperature must be increased. Therefore, the gas temperature inside the combustion chamber needs to be maintained at a very high level. Hence, cooling of the combustor liner becomes critical. Among all the cooling techniques, film cooling has been successfully applied to cool the combustor liner. In film cooling, coolant air is introduced through discrete holes and forms a thin film between the hot gases and the inner surface of the liner, so that the inner wall can be protected from overheating. The film will be destroyed in the downstream flow because of mixing of hot and cold gases. The present work focuses on numerical study of film cooling under operating conditions, i.e., high temperature and pressure. The effect of coolant injection angles and blowing ratios on film cooling effectiveness is studied. A promising technology, cooling with mist injection, is studied under operating conditions. The effect of droplet size and mist concentration is also analyzed. The results of this study indicate that the film cooling effectiveness can increase ∼11% at gas turbine operating conditions with mist injection of 2% coolant air when droplets of 10μm and a blowing ratio of 1.0 are applied. The cooling performance can be further improved by higher mist concentration. The commercial CFD software, Fluent 6.3.26, is used in this study and the standard k-ε model with enhanced wall functions is adopted as the turbulence model.

Critical heat flux (CHF) of convective boiling in a mini-tube due to power transient was measured. A platinum tube with an inner diameter of 1.0 mm was heated exponentially by a direct current power supply as Joule heating. The heated length of the platinum tube was 40.9 mm. The platinum tube was mounted vertically in the water-loop apparatus which consisted of a circulating pump, a pre-heater, a flow mater, a pressurizer, a cooler and a test section. The deionized water was pressurized by the pressurizer up to approximately 800 kPa to measure CHFs at the high subcooling. The upward flow velocity in the platinum tube was ranged from 5 to 11 m/s. The inlet subcooling was ranged from 92 to 117 K. The heat generation rate was controlled with exponential functions. The e-folding time of the heat generation rate was ranged from 30 ms to 18 s. As an experimental result, it was found that the CHFs increased with increasing the flow velocity and the inlet subcooling. The CHF also increased with decreasing the e-folding time of the heat generation rate. Since the heat generation rate of the platinum tube increased rapidly under the power transient condition, it was considered that the heat flux of the platinum tube increased until the vapor blanket covered the heated surface of the platinum tube.

In order to improve pipes and valves maintenance in EDF power plants by the use of reliability analysis, some wear mechanisms have been listed and their wear kinetics have been investigated. One of these wear mechanisms is cavitation erosion. Cavitation may occur in numerous pipe components such as valves, orifices, elbows and tees, in any place where low pressure and/or high velocity is reached. The effects of cavitation developments are first noise and vibrations, then erosion of the downstream pipe if the material is not resistant enough and at least loss of performance of the component (choking). A predictive model to evaluate cavitation erosion in valves and pipes was proposed in 1998 by Lecoffre [4]. Experiments on a closed cavitation test loop for the simple geometry of two sharp-edge single hole orifices (opening factor β = d/D = 0.4 and β = d/D = 0.8) have been performed in order to validate this model. First, the cavitation developments downstream the orifice have been visualized through a transparent pipe section. Incipient and chocking pressure coefficient have been recorded and compared with data from Tullis [2]. Then the erosion has been quantified using pitting measurements on mirror polished 316L stainless steel samples, located flush on the inner pipe surface. Cavitation pits have been measured using a laser profilometer. The plastic deformation volume measurement allows to define a pitting velocity, which can be related to a « loss of thickness » velocity, taking into account previous erosion tests on the pipe material. These pitting tests were performed for five flow conditions, characterized by three flow rate values and three pressure coefficient values. In the predictive model, these flow conditions parameters are more precisely defined by the flow velocity in the contracted section, named V1 (m/s), and by the pressure coefficient calculated with the lowest pressure in the contracted section, named σ1 (-). At least, a predictive model was adjusted using these experimental results. We found that the cavitation erosion wear velocity of a 316L stainless steel straight pipe downstream the orifice (characterized by its opening factor β) for the flow condition (σ1, V1) with cavitation σ1&lt;1 fits well to the following formula: Verosion=k.(1−σ1)6.8.(V1−V0)5 with : k = f(β), V0 = g(β) where f and g are functions of the opening factor β = d/D. Tests using the same methodology have since been performed on butterfly valves and on multiholes orifices.

The compression process in a piston cylinder device in a Compressed Air Energy Storage (CAES) system is studied computationally. Twelve different cases featuring four different compression space length-to-radius aspect ratios and three different Reynolds numbers are studied computationally using the commercial CFD code ANSYS FLUENT. The solutions show that for compression with a constant velocity, the compression can be approximated by a polytropic pressure vs. volume relation. The polytropic exponent, n, characterizes the heat transfer and temperature rise of the air being compressed. For the cases computed, it varies from 1.124 to 1.305 and is found to be more affected by Reynolds number and less by the length-to-radius ratio. Since the efficiency and storage power of the compressor depend on pressure vs. volume trajectory during compression, they are written as functions of the pressure rise ratio and the polytropic exponent, n. The efficiency is high at the beginning of the compression process, and decreases as the compression proceeds. The effect of temperature rise or heat transfer on efficiency and storage power is shown by comparing the efficiency and storage power vs. volume curves having different n values. Smaller temperature rise always results in higher efficiency but lower dimensionless storage power for the same compression pressure ratio. The storage power is used in this study to distinguish the compression process effect (n effect) and the compressor’s size effect on the storage power. The likelihood of flow transitioning into turbulent flow is discussed. A k–ε Reynolds Averaged Navier Stokes (RANS) turbulence model is used to calculate one of the larger Reynolds number cases. The calculated polytropic exponent was only 0.02 different from that of the laminar flow solution. The CFD results show also that during compression, complex vorticity patterns develop, which help mix the cold fluid near the wall with the hot fluid in the inner region, beneficial to achieving a higher efficiency.

A core-shell elasticity model is employed to investigate the effect of a nanowire and nanotube’s increased surface moduli on specific heat, ballistic thermal conductance, and thermal conductivity as a function of temperature. Phonon confinement is analyzed using approximated phonon dispersion relations that result from solutions to the frequency equation of a vibrating rod and tube. The results indicate a maximum 10% decrease in lattice thermal conductivity and ballistic thermal conductance near 160 K for a 10 nm outer diameter nanotube with an inner diameter of 5 nm when the average Young’s Modulus of both the inner and outer free surfaces is increased by a factor of 1.53. In the presence of the acoustically stiffened surfaces, the specific heat of the nanotube is found to decrease by up to 20% at 160 K. Near room temperature, changes in thermal properties are less severe. In contrast, a 10 nm outer diameter nanowire composed of similar material exhibits up to a 12% maximum increase in thermal conductivity at 600 K, a 25% increase in ballistic thermal conductance at 400 K, and a 48% increase in specific heat at 470 K when its outer free surface is acoustically stiffened to the same degree. Our simplified model may be extended to investigate the acoustic tuning of nanowires and nanotubes by inducing surface stiffening or softening via appropriate surface chemical functionalization and coatings.