Suppose in general that ϕ = 0, Ψ = 0, See.denote a system of ( n — 1) equations between the n variables ( x, y, z ,..), where the functions ϕ , Ψ , &c. are quantics ( i. e . rational and integral ... z 2 ..) of the remaining ( n — 1) equations Ψ = 0 X = 0, &c.; comparing such expression with ... in terms of the coefficients of the functions Ψ X , &c.., certain symmetric functions which may be ... symmetric functions of the roots of the system Ψ = 0 X = 0, &c., these are in fact ... symmetric functions of the roots of the system Ψ = 0 X = 0, &c.. maybe expressed in terms ...
Tópico(s): Functional Equations Stability Results
1857 - Royal Society | Philosophical Transactions of the Royal Society of London
Die Berechnung von Zweizentrenintegralen mit wasserstoffähnlichen 2s-Funktionen: ψs′ = N [ β ψ k -ψ s ], (mit ψ k = δ 3/2 π -1/2 exp. (-δr); ψ s . = δ 5/2 (3 π) -1/2 ... Funktionen zerfällt in die Berechnung von Integralen, die ψ k bzw. ψ s und ψ p enthalten. Orthogonalitäts-, Übergangs-, Austausch-, Coulomb- und Ionen-Integrale mit ψ k und ψ s und ψ p werden für gleiche effektive ...
Tópico(s): Synthesis and properties of polymers
1952 - De Gruyter | Zeitschrift für Naturforschung A
... of the type k (ξ 1 ... ξ n ) = ∫ -∞ ∞ ... ∫ -∞ ∞ ψ ( x 1 ... x n ) L (ξ 1 -x ... x n , where L is L -integrable, and ψ and k are bounded. Since rapidly oscillating ψ have a small k , and since measurements of ... non-zero limits of experimental error, very different ψ are consistent with any given set of measurements of k . Thus ψ is not determined by measurements of k . Instead of ψ, partial information about ψ that is not sensitive to rapid oscillations of ψ, can be obtained from k . In the present paper we consider smoothed versions of ψ, and their applications to gravity survey and the ...
Tópico(s): Mathematical functions and polynomials
1949 - Royal Society | Proceedings of the Royal Society of London A Mathematical and Physical Sciences
... N Ʃ i > j = 1/ r ij -E} Ψ = 0, using atomic units11 and the usual notation. ... 1 (-1/2∇ i 2 - v i ) -E} ψ = 0, V i being a function of the ... 1/2∇ i 2 - v i ) -E i } ψ = 0, in the space co-ordinates of the - ... If the solutions of equations (1. 3) are Ψ(α∣1), Ψ(π|p), where the Greek letter is the ... substituted, then a solution of (1. 2) is ψ = Ψ(α∣1) Ψ (β∣2)....Ψ(π|p). The form of wave function which ... all pairs of electrons, is the determinantal form Ψ = ∣ψ = Ψ(α∣1) Ψ (α∣2)....Ψ( ...
Tópico(s): Advanced Physical and Chemical Molecular Interactions
1932 - Royal Society | Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character
... its unperturbed state by a determinantal wave function Ψ 1 (as in equation (3·1) of Paper I), containing electronic functions of the type Ψ p 1 p 3 where p 1 may ... of the p th electron are inserted in Ψ P1P > Similarly the second atom contains N 2 ... represented in its unperturbed state by a determinant Ψ 2, containing functions Ψ p 2 r , where p 2 may be ... of the unperturbed system of two atoms is Ψ = Ψ 1 Ψ 2 f Ψ * Ψ dr = N 1 ! N 2 !, where the integration ...
Tópico(s): Advanced Physical and Chemical Molecular Interactions
1937 - Royal Society | Proceedings of the Royal Society of London A Mathematical and Physical Sciences
Samuel Karlin, Albert Novikoff,
... inequalities with the aid of certain auxiliary functions ψ 19 •• ,φ k f or locally, if φ ... the latter case smoothness hypotheses are imposed on ψ 19, ψ k in order to define the relevant differential ... dμ (not necessarily nonnegative) which are orthogonal to ψ l9 •••, ψ k9 and in addition satisfy an inequality described ... the minimal oscillation compatible with being orthogonal to ψ l9, ψ k , a condition depending on k but not otherwise on the choice of ψ l9, ψ k (see Lemma B).In the first section ... somewhat different.We introduce the general cones C(ψ l9 , ψ k ) in § 3 where for ease ...
Tópico(s): Functional Equations Stability Results
1963 - Mathematical Sciences Publishers | Pacific Journal of Mathematics
... p̄ = P/Ab and the specific friction force ψ = F/Ab. Hence μ = F/P = ψ/p̄. It will be shown in this paper ... smooth sliding is caused by the decrease of ψ with rising T. The specific friction force is ... constψ(T), which makes it possible to study ψ as a function of T by studying μ as a function of T. The decrease of ψ with rising T is explained by assuming that ... kT. Hence it is expected that μ and ψ are inversely proportional to the probability factor. It ... to about 500°K (the upper limit measured): ψ(T)ψ(T0)=μ(T)μ(T0)=exp[ ...
Tópico(s): Electrical Contact Performance and Analysis
1962 - American Institute of Physics | Journal of Applied Physics
S.A. Gavande, Sterling A. Taylor,
... for a second series. Total plant water potential (ψ), osmotic potential (ψ a ), and relative turgidity were determined directly. Turgor potential was determined by the differences (ψ p ═ ψ – ψ a ) in leaf sections from plants grown under ... addition, transpiration loss rates and soil water potentials (ψ s ) were measured daily. The total plant water potential (ψ), the osmotic potential (ψ a ), turgor potential (ψ p ), and transpiration losses from the two plant species were influenced by soil water potential (ψ s ) and AED. The effect was greater on ...
Tópico(s): Irrigation Practices and Water Management
1967 - Wiley | Agronomy Journal
... unit disk D = {z: \ z \ < 1}.A function ψ in H °° is called a generator if the polynomials in ψ are weak-star dense in H°*.The problem ... following way.By Fatou's theorem, each function ψ in H°° has radial limits at almost every ... thus gives rise to a bounded measurable function ψ a on C. The map ψ -• ψ σ sends H°° isomorphically and isometrically onto a ... topology are easily characterized.LEMMA 1.A sequence {ψ n }T in H°* converges weak-star to the function ψ if and only if it is uniformly bounded and converges to ψ at every point of D. 11az IWe then ...
Tópico(s): Nonlinear Waves and Solitons
1966 - Mathematical Sciences Publishers | Pacific Journal of Mathematics
... were grown in the presence of labeled pseudouridine (Ψ uridine) and suboptimal amounts of uracil. During one doubling time a small amount of Ψ uridine was taken up, and radioactivity appeared in ... these compounds indicated that little dilution of fed Ψ uridine had occurred in the pool. In RNA, label appeared mainly in the pyrimidines, with Ψ uridine being the most highly labeled. Appearance of ... a limited ability of the organism to degrade Ψ uridine. The specific activities of Ψ uridine isolated from the various RNA fractions and ...
Tópico(s): DNA and Nucleic Acid Chemistry
1968 - Elsevier BV | Journal of Biological Chemistry
... denoted by ∘, forming the union of two states; ψ ∘φ denotes the state of a compound system whose parts are in the states ψ and φ. Let ψ and φ denote 1-particle states and assume: (a) ψ ∘φ exists whenever ψ ⊥ φ; (b) ψ ∘φ=φ ∘ψ; (c) the transition probability between ψ ∘φ and ψ′ ∘φ′ is zero if ψ ⊥ ψ′ and ψ ⊥ φ′, and (d) the product ...
Tópico(s): Advanced Thermodynamics and Statistical Mechanics
1968 - American Institute of Physics | Journal of Mathematical Physics
... and the spectrum of f.(The spectrum of ψ is the set S(ψ) = {λ : f(λ + e)-f(λ -e)>0 ... we identify all functions which agree on S(ψ).In [2], (p.215), Carleman showed that the ... X 1/V b { = oo implies that when ψ is normalized to be continuous from the left and to have ijr(-co) = 0, ψ( + ) -1, then it is unique.In [6], M. Riesz showed that if ψ is essentially unique then ParsevaFs relation holds for the orthonormal set {P { } in the space ^f2 {ψ).Hence the set {PJ is dense in this ... result and the Riesz result we see that ψ is essentially unique and the polynomials {P<} are ...
Tópico(s): Matrix Theory and Algorithms
1969 - Mathematical Sciences Publishers | Pacific Journal of Mathematics
J. O’M. Bockris, M. A. Genshaw, V. Brusić, H. Wroblowa,
... unidirectional scratches gave different values of Δ and ψ if the position of the sample was changed ... respect to the oncoming light; apparent Δ and ψ were dependent also on the degree of polishing. ... min and i > 10 μA/cm2, Δ and ψ changed with time and the original values were ... A sufficient degree of polishing gave Δ and ψ for oxide-free iron in solution, which showed ... Fe2+ : Fe3+ in the film. Δ/potential and ψ/potential relations showed three regions; pre-peak, peak ... and 0–900 mV(she). Δ/potential and ψ/potential relations measured at short (1 s) and ...
Tópico(s): Gold and Silver Nanoparticles Synthesis and Applications
1971 - Elsevier BV | Electrochimica Acta
V. V. Bochkarev, G.B. Radzievsky, Lev Timofeev, N.A. Demianov,
... work is to determine the point source functions ψ(r) for beta-radiation with energies in the ... conditions that must be satisfied by the functions ψ(r) are formulated and possible methods of finding ... of Spencer's theory). In order to determine ψ(r) we have found first the values of the function ψ(r, Ei) for an isotropic point source of monoenergetic electrons of energy Ei. For ψ(r, Ei) we have used experimental data and ... distribution approximation" (scaling law for dose distributions). The ψ(r) functions for 14 beta sources were obtained ...
Tópico(s): Nuclear Physics and Applications
1972 - Pergamon Press | The International Journal of Applied Radiation and Isotopes
I. F. Ike, G. W. Thurtell, K. R. STEVENSON,
... in cassava (Manihot esculenta Crantz). Xylem pressure potentials (ψ P ) measured with the pressure chamber were compared with leaf water potential (ψ L ) obtained for the same leaf with the ... dew-point hygrometer.In both cassava varieties studied, ψ L and ψ P were linearly related (r 2 = 0.87 ... exposed outside the chamber affects the relation between ψ L and ψ P and should be kept at between 1 and 3 cm for better agreement. In CMC40, ψ P was consistently lower (drier) than ψ L by about 1.0 bar (1 bar = ... xylem tissues (Boyer 1967) during the measurement of ψ P in CMC40. Average xylem osmotic potentials (ψ ...
Tópico(s): Spectroscopy and Chemometric Analyses
1978 - Canadian Science Publishing | Canadian Journal of Botany
Kenneth C. Kuo, Charles W. Gehrke, Roy A. McCune, T. Phillip Waalkes, Ernest Borek,
... chromatographic method for the determination of pseudo-uridine (ψ) in urine by high-performance liquid chromatography (HPLC) ... gel containing immobilized phenylboronic acid. The response for ψ was linear well above and below the range necessary to determine urinary ψ. Good precision was obtained for both matrix-dependent ... patients, 9 of the 10 patients had a ψ: creatinine (Cr) ratio greater than x̄ + 2σ for ... laboratory as a routine method for determination of ψ in urine from patients with various types of ...
Tópico(s): Folate and B Vitamins Research
1978 - Elsevier BV | Journal of Chromatography B Biomedical Sciences and Applications
James O. MAXWELL, R. E. Redmann,
Abstract Water (ψ), osmotic (ψ s +ψ m ) and pressure (ψ p ) potentials were measured in three leaf regions of Agropyron dasystachyum and A. smithii grown in the field. Spanner‐type thermocouple psychrometers were used to measure ψ and (ψ m +ψ m ). Absolute water content (AWC) was measured gravimetrically. The ψ and ψ p were slightly lower in the emerging leaf ... in the last fully emerged leaf blade (FEBI); (ψ s +ψ m ) and AWC were similar in ...
Tópico(s): Soil and Unsaturated Flow
1978 - Wiley | Physiologia Plantarum
W. L. Ehrler, Sherwood B. Idso, Ray D. Jackson, R. J. Reginato,
... and simply by determining the plant water potential (Ψ plant ). This experiment was undertaken to demonstrate that crop canopy temperature responds specifically to changes in Ψ plant and therefore can be used for long ... plant canopy and air (ΔT) was related to Ψ plant , as shown by simultaneous, daily measurements of ... just before sunrise) and 1400 hours. At predawn, Ψ plant ranged from −2.0 bars in recently ... point (θ v = 0.15). At 1400 hours, Ψ plant ranged from −15 bars when θ v ... was −3.8 C at full plant hydration (Ψ plant = −15 bars). Increasing drought decreased Ψ plant ...
Tópico(s): Greenhouse Technology and Climate Control
1978 - Wiley | Agronomy Journal
... A cell‐produced chemical factor extracted from Naegleria, Ψ, triggers a reproducible sequence of rapid shape changes ... environment. Cells respond to the presence of external Ψ only “transiently,” and the reaction of flagellates to added Ψ requires extracellular Ca +2 . Ionophore A23187 produces shape changes in flagellates similar to those produced by Ψ, supporting the conclusion that Ψ is involved in the movement of Ca +2 . Normally Ψ is intracellular, and the intracellular distribution of Ψ changes during differentiation. These results lead to and ...
Tópico(s): Bacterial biofilms and quorum sensing
1977 - Wiley | Journal of Supramolecular Structure
... the semi-classical structure of the Wigner functions Ψ( q,p ) representing bound energy eigenstates | Ψ 〉 for systems with f degrees of freedom. If ... classical motion is integrable, the classical limit of Ψ is a delta function on the f -dimensional torus to which classical trajectories corresponding to |Ψ〉 are confined in the 2 f -dimensional phase space. In the semi-classical limit of Ψ ( ℏ small but not zero) the delta function softens to a peak of order Ψ− f and the torus develops fringes of a characteristic ‘Airy’ form. Away from the torus,Ψ can have semi-classical singularities that are not ...
Tópico(s): Nuclear physics research studies
1977 - Royal Society | Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences
C. K. CHU, U. REICHMAN, Kyoichi A. Watanabe, Jack J. Fox,
Abstract 2′‐Deoxy‐ψ‐isocytidine (VIIβ), a 2′‐deoxy analog of antileukemic ψ‐isocytidine and also a C ‐nucleoside analog of deoxycytidine, was synthesized from ψ‐uridine by making use of the newly discovered ... J. Chem. Soc. , 14, 537 (1977)]. 2′‐Deoxy‐ψ‐uridine (IIβ) and 2′‐deoxy‐l‐methyl‐ψ‐uridine (V), both C ‐nucleoside analogs of deoxyuridine and thymidine, were also synthesized. ψ‐Uridine was converted into the 2′‐chloro analogs ( ... give an α,β‐mixture of 2′‐deoxy‐ψ‐uridines. The β‐isomer (11β was trimethylsilylated and ...
Tópico(s): Biochemical and Molecular Research
1977 - Wiley | Journal of Heterocyclic Chemistry
W. Bartel, P. Duinker, J.E. Olsson, P. Steffen, J. Heintze, G. Heinzelmann, R.D. Heuer, R. Mundhenke, H. Rieseberg, B. Schürlein, A. Wagner, A.H. Walenta,
Decays of the J/ψ (3.1) resonance into final states with two charged hadrons and two photons are investigated. Branching ratios for the decays J/ψ → ϱπ and J/ψ → γη′ are determined to be Г(J/ψ → pφ)Г(J/ψ → all) = (1.0± 0.2) ·10−2, Г(J/ψ → γη′)ГJ/ψ → all) = (2.0± 0.7) ·−3 Upper limits for the same decay modes of ψ′ (3.7) are also determined.
Tópico(s): Atomic and Subatomic Physics Research
1976 - Elsevier BV | Physics Letters B
... a definite point. For an incomplete measured θ(ψ) loop the knowledge of K at the minimum measured value of ψ can be used to improve prediction. The dependent ... 1975) is generalized by adding two functions KL(ψ) and KH(ψ) . All K(ψ) scanning curves are expressed with the aid of KL(ψ) and KH (ψ) by convenient compact formulation similar to that used to describe the θ(ψ) curves. The theory is verified by comparison with ... theory and observations is found. The predicted K(ψ) hysteresis has all the experimentally observed features. The ...
Tópico(s): Soil Moisture and Remote Sensing
1976 - Wiley | Water Resources Research
... days old, the potential of the root medium (ψ r ) was lowered by 1 bar every second ... bar. By regression it was found that when ψ r was lowered by I bar, osmotic potential in leaf (ψ π ) decreased 1.46 bar, and leaf water potential (ψ t ) 0.68 bar, which mean an increase ... dry matter. Specific transpiration rate increased significantly after ψ r was kept constant, but the increase in ... old leaves. After an “adaptation” period during which ψ r remained at −0.7, −4, and −7 bar, respectively, for at least 1 week. ψ r was altered so as to cover the ...
Tópico(s): Magnetic and Electromagnetic Effects
1976 - Wiley | Physiologia Plantarum
... X by X(1) ,…, X(k) and set ψ(0)(S, X) = {(n − p + 2)!(n + 2)!} | S |, ψ(i)(X, X) = min[ψ(i−1)(S, X), {(n − p + i + 2)!( ... 1) X′(1) + ⋯ + X(i) X′(i) |] and Ψ(i)(S, X) = min[ψ(0)(S, X), {(n − p + i + 2)!(n + ... is that the minimax, best affine equivariant estimator ψ(0)(S, X) is dominated by each of Ψ(i)(S, X), i = 1,…,k and for every i, ψ(i)(S, X) is better than ψ(i−1)(S, X). In particular, ψ(k)(S, X) = min[{(n − p + 2)!(n + ...
Tópico(s): Advanced Statistical Methods and Models
1976 - Elsevier BV | Journal of Multivariate Analysis
... 2.8 GeV state, the large rates for ψ′ → ψη, ψ → η′γ and ψ → ηψ, the large number of photons in ψ decay, some of the missing decay modes of ψ′ and ψ and the small K/π ratio in ψ′ and ψ decays. We predict that 20–30% of all ψ and ψ′ decays contain an η′. Other tests and one ...
Tópico(s): High-Energy Particle Collisions Research
1976 - Elsevier BV | Physics Letters B
Abstract The water potential (ψ) in twigs from four clones of Scots pine ( Pinus sylvestris L.) growing in close proximity to each other was measured ... and March 1973. Diurnal and seasonal patterns of ψ are presented in relation to irradiance, air temperature ... day in each experimental period. Significant differences in ψ were found amongst most of the clones. Larger amplitudes and earlier day‐time minima in ψ were found during the summer than during the winter. Noon values of ψ of less than −12 bars were regularly found ...
Tópico(s): Forest ecology and management
1976 - Wiley | Physiologia Plantarum
R. N. Cahn, Michael S. Chanowitz,
... the Okubo-Iizuka-Zweig rule for decays of Ψ and Ψ′ suggests that the radiative decays Ψ → γ + hadrons should be dominated by intermediates like Ψ → Ψ′ hadrons. This mechanism is consistent with experimental data which show Γ(Ψ → ϱ0π0) and Γ(Ψ → ηγ) to be comparable. if all Ψ-like particles are isoscalar, Γ(Ψ → 0γ) should be very small. If all Ψ- ...
Tópico(s): Black Holes and Theoretical Physics
1975 - Elsevier BV | Physics Letters B
Let ψ 0 ( x ) ∈ S ( R n ) {\psi _0}(x)\, \in \,{\mathcal {S(}}{R^n}{\text {)}} and let ∫ R n ψ 0 ( y ) d y ≠ 0 \int _{{R^n}} {{\ ... 0 , let \[ f + ( x ) = sup t > 0 | f ∗ ψ 0 t ( x ) | {f^ + }(x)\, = \,\sup \limits _{t\, > \, ... right | \] and let f ∗ M ( x ) = sup { | f ∗ ψ t ( x ) | : t > 0 {f^{{\ast }M}}(x)\, = \,\ ... f\,{\ast }\,{\psi _t}(x)} \right |:\,t\, > \,0 , ψ ( y ) ∈ S ( R n ) \psi (y)\, \in \,{\mathcal {S(}}{R^n}) , supp ψ ⊂ { y ∈ R n : | y | > 1 } \operatorname {supp} \,\psi \, \ ... R^n}:\,\left | y \right |\, > \,1\} , ‖ D α ψ ‖ L ∞ ⩽ 1 {\left \| {{D^\alpha }\psi } \right \|_{{L^\ ... i = 1}^n\,{\alpha _i}\, \leqslant \,M\} where ψ t ( y ) = t − n ψ ( y / t ) {\psi _t}(y)\, = \,{t^{ - n}}\psi ( ... and C are positive constants depending only on ψ 0 {\psi _0} , p, M and n . We ...
Tópico(s): Mathematical Analysis and Transform Methods
1980 - American Mathematical Society | Transactions of the American Mathematical Society
A. Ben-Aziz, George Britton, T. W. Goodwin,
... of lycopene (1,2-epoxy-1,2-dihydro-ψ,ψ-carotene and 5,6-epoxy-5,6-dihydro-ψ,ψ-carotene). The other related compounds have been identified ... 8,11,12,7′,8′,11′,12′-decahydro-ψ, ψ-carotene), phytofluene (1,2-epoxy-1,2,7,8, 11,12,7′,8′-octahydro-ψ,ψ-carotene and 1,2-epoxy-1,2,7,8,7′,8′,11′,12′-octahydro-ψ,ψ-carotene) and ξ-carotene (1,2-epoxy-1, ...
Tópico(s): Insect Pheromone Research and Control
1973 - Elsevier BV | Phytochemistry