... problems, conditions for positiveness of Greens functions, and solutions with various BCs, for example, NBCs The structure of the paper is as follows In Section 2, we review the properties of functional ... discrete initial conditions We apply these results to BVPs with NBCs: first, we construct theGreensfunctionfor classical BCs, then we can construct Greensfunctionfor a problem with NBCs ... determinants and linear functionals We construct a special basis of the solutions in Section and introduce some functions that are independent of this basis The expression of the solution to the second-order...
... • Sources in a session should be visible at the same time for at least to hours • Sources with Declinations less than the latitude of the GBT should not be in the same session as sources with ... dual-beam systems (i.e., two feeds); hence there are always two beams on the sky Nodding is usually used for these systems (see § 4.2) The continuum point-source sensitivity depends on three factors These ... not show the strength of these signals very well as they overpower the system Observers should consult the support scientists before submitting a proposal for this feed C-band Receiver The C-band...
... cytosol-specific isoenzymes in spinach Since then, the isoforms of ATP-PFK from various plant sources have been studied [23–34] Spinach cytosolic ATP-PFK is activated by 25 mm phosphate, whereas the ... phosphofructokinase Amycolatopsis methanolica, possess two very distinct PFK types [7] Within group II, SoPFK1 clustered with Oryza sativa and Arabidopsis thaliana PFK homologs, as does SoPFK2 (Fig 5B) In sequence ... and other plants [27] These Fig Spinach PFK activity assayed in the absence (black bar) or presence (gray bar) of 25 mM phosphate The white bar shows pyrophosphate:fructose-6-phosphate 1-phosphofructokinase...
... then be well-defined as its density The conductivity measure ΣEF (dν) is thus an analogous concept to the density of states measure N (dE), whose formal density is the density of states n(E) The ... t)ψ(t) A similar statement holds in the opposite direction for weak solutions (See the discussion in [BoGKS, Subsection 2.2].) At the formal level, one can easily see that the linear response current ... Wegner s estimate forthe density of states [W] The finite volume expression is then controlled by Minami s estimate [M], a crucial ingredient Combining all these estimates, and choosing the size...
... arithmetic subgroup An important problem in the theory of automorphic forms is the question of the existence and the construction of cusp forms for Γ By Langlands’ theory of Eisenstein series [La], cusp ... poles of Rankin-Selberg L-functions in the critical strip We use these results in Section to establish the key estimates forthe logarithmic derivatives of normalizing factors In Section we study ... sij satisfy | Re(sij )| < 1/2 and the rij s are integers The proof in the case F = R is essentially the same We only have to check the different possible cases forthe L-factors as listed above...
... taxes, securities gains or losses, and extraor dinary items, plus the provision for possible loan and lease losses divided by net loan and lease losses If gross recoveries exceed gross losses, ... loans and leases If gross recoveries exceed gross losses, NA is shown at this caption Gross Loss to Average Total Loans & Leases Gross loan and lease losses divided by average total loans and ... leases), other real estate owned, acceptances and other assets divided by average total assets Total Assets Assets, Percent of Average Assets Loans Held For Sale Average loans and leases held for...
... Fowls and goats seem the only other means of subsistence of these people The geological features of the country are easily described Vast masses of granite rock are scattered along the coast; for ... daily visited by crowds of canoes filled with necessaries or curiosities Fowls, eggs, yams, cocoa-nuts, and sweet potatoes, were mixed with monkeys of various sorts, paroquets, squirrels, shells, ... discovery in prospectu possesses great attractions forthe imagination, the hardship, danger, and thousand other rude realities, soon dissipate the illusion, and leave the aspirant longing for...
... H) The authors want to emphasis that for n = 1, the result is classical; for n = 2, Theorem 2.6 leads to Theorem 1.1 Shen also shows by providing an example that minimal number of spectral sets ... denotes the determinant of A In the remaining of this section, we shall prove some uniqueness theorems for vectorial Sturm-Liouville equations Let B(i, j) = brs brs = 0, 1, (r, s) = (i, j), (r, s) ... above theorem forthe case m ≥ The idea we use is the Weyl s matrix for matrix-valued Sturm-Liouville equation Y + (λIm − Q(x))Y = 0, < x < π (1:5) Some uniqueness theorems for vectorial Sturm-Liouville...
... [14] has also studied a class of small deviation theorems forthe sequences of N-valued random variables with respect to mthorder nonhomogeneous Markov chains In this paper, our main purpose is to ... class of small deviation theorems for functional of random fields on a homogeneous tree J Math Anal Appl 361, 293–301 (2009) 14 Yang, WG: A class of small deviation theorems forthe sequences ... predecessor of (n - 1)t by nt We also say that nt is the n-th predecessor of t XA = {Xt, t Î A} is a stochastic process indexed by a set A, and denoted by |A| the number of vertices of A, xA is the...
... and e(t) is a continuous function on [0, T] It is well known that the solutions of (3) can be expressed in the following forms T u(t) = G(t, s) e (s) ds, where G(t, s) is Greensfunction associated ... ρ ≤ 3π 2T (2) is a constant and the associated Greensfunction may changes sign The aim is to prove the existence of positive solutions to the problem Preliminaries Consider the periodic boundary ... expressed sin ρ(t s) +sin ρ(T−t +s) , 2ρ(1−cos ρT) sin ρ (s t)+sin ρ(T s+ t) , 2ρ(1−cos ρT) G(t, s) = ≤ s ≤ t ≤ T, ≤ t ≤ s ≤ T By direct computation, we get ρT sin sin ρT ≤ G(t, s) ≤ = max G(t, s) ,...
... t G1 t, s r s f s, ys t∈ 1,T t∈ 1,T ≥m us s T r s f s, ys us s ≥ ≥ which implies that Φ K ⊂ K m T Ms max G1 t, s 1 s, t≤T r s f s, ys T m max G1 t, s r s f s, ys M t∈ 1,T s m Φy , M us us 3.15 ... Then BVP 3.1 has at least one positive solution if the following conditions are satisfied: H4 there exists a p1 > h such that, fors ∈ 1, T , if φ τ ≤ p1 h, then f s, φ ≤ R1 p1 ; H5 there exists ... implies that 2.36 has a unique solution c1 c2 Therefore v t ≡ w t for t ∈ −τ, T This completes the proof of the uniqueness of the solution 10 Boundary Value Problems Existence of Positive Solutions...