Analytical two-center integrals over Slater geminal functions

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-\gamma r12) term in the master integral.Comment: 28 pages, 0 figures, 7 table

ROOT ZONE TEMPERATURE AFFECTS EMERGENCE AND GROWTH TRAITS OF SNAKE TOMATO (TRICHOSANTHES CUCUMERINA L.)

Two Nigerian morphological variants of Trichosanthes cucumerina L., (Cucurbitaceae) an under-exploited tropical leaf and fruit vegetable were evaluated for response to root zone temperature (RZT) in a climate controlled growth chamber at 20, 25 and 30 oC. The Green variant [V1] has long fruit with deep green background and white stripes at unripe stage while Light Green variant [V2] has light green coloured long fruit when at unripe stage. Results showed that the first emergence for seeds at RZT of 30 oC occurred at 7 days after planting (DAP) for both variants while those planted at RZT of 20 oC and 25 oC showed first emergence at 10 and 14 DAP, respectively. At RZT of 20 oC, 25 oC and 30 oC, days to 50% emergence were 18, 12 and 8 DAP while last emergence was registered at 24, 15 and 10 DAP, respectively. This work showed that under controlled growth chamber conditions, days to first emergence was reduced by 5 days compared to the 12 DAP recorded under tropical field conditions. Root zone temperatures (T) produced statistically significant (P ≤ 0.05) effects on the average number of tendrils, number of leaves, fresh leaf weight, stem length, fresh stem weight, root length, root weight and root volume while the main effect of T. cucumerina variants (V) and the interaction (V x T) produced no significant effects on all the parameters measured. The values recorded for each of the growth parameters were only numerically higher in the Green Variant (V1) compared to Light Green Variant (V2). The significantly highest value for each of the growth traits were recorded at 30 oC followed by 25 oC and 20 oC, in that order. Low root zone temperature of 20 oC produced adverse effects on both emergence and growth of T. cucumerina. This study established the need for providing soil warming facility for a successful cultivation of T. cucumerina in chilly (temperate) environment

UV-B induced damage and recovery processes in apple leaves as assessed by LIF and PAM fluorescence techniques

The capability of laser-induced chlorophyll fluorescence (LIF) and pulse-amplitude-modulated (PAM) fluorescence technique as well as RED/NIR-light reflection measurements for detection and quantification of UV-B induced damages was evaluated in greenhouse experiments with apple seedlings (Malus domestica Borkh.). Photosynthetic recovery from short-term UV-B stress was assessed during 7 days after UV-B treatment with the PAM fluorometer. The exposure of apple leaves to UV-B doses in the range of 10-26 W m-2 for 180 minutes (UV-BBE dose = 5.4-14 kJ m-2) affected neither chlorophyll content nor leaf reflection. Although UV-B damage was not visually evident 2 hours after irradiation, it could be detected by PAM and LIF fluorescence techniques with equivalent success. The intensity of LIF, estimated as the integral of fluorescence spectrum, was reduced after UV-B irradiation by 19-30%. A stronger decrease in F686 compared to F740 fluorescence resulted in significantly lower F686/F740 values in all UV-B treatments.Apple leaves displayed a strong and significant reduction in maximum fluorescence (Fm) and a slightly increase in ground fluorescence (Fo) 2 hours after UV-B treatment, as documented by PAM fluorescence measurement. Negative linear regressions between investigated UV-B doses and selected PAM parameters were found with determination coefficients (R2) of 0.50 for Fv, 0.48 for Fv/Fm, and 0.58 for Fv/Fo. Among the PAM and LIF parameters tested, the Fv/Fo ratio appeared most sensitive for detection of UV-B induced damages displaying greatest changes and strongest correlation with the applied UV-B doses. PAM fluorescence images of apple leaves visualised an enhanced spatial heterogeneity of photosynthetic activity with increasing UV-B dose. The disturbance in photosynthetic functionality was followed by a continuous recovery process as indicated by restoring Fo and Fm parameters. A decline in maximum photochemical efficiency Fv/Fm from 0.80 to 0.72 and 0.43 after exposure to 20 W m-2 for 240 and 360 minutes (UV-BBE = 14.4 and 21.6 kJ m-2), respectively, was followed by recovery at 7 x 10-4 and 5 x 10-3 units per hour during the first 48 hours after UV-B treatment. The recovery curves of Fm, Fv, Fv/Fm and Fv/Fo parameters during a week after UV-B irradiation were well fitted with exponential rise to maximum function, such as: y = yo + a (1 - e-bx). However, within 7 days after exposure to UV-B light, apple leaves displayed 14% or 4% lower Fm, and 5% or 1% lower Fv/Fm values compared with control plants, indicating only a partial recovery from photoinhibition and irreversible damages in PSII

Point selections and weak e-nets for convex hulls

One of our results: let X be a finite set on the plane, 0 < g < 1, then there exists a set F (a weak g-net) of size at most 7/e 2 such that every convex set containing at least e\X\ elements of X intersects F. Note that the size of F is independent of the size of X. 1

Review of the History and Current Status of Cell-Transplant Approaches for the Management of Neuropathic Pain

Treatment of sensory neuropathies, whether inherited or caused by trauma, the progress of diabetes, or other disease states, are among the most difficult problems in modern clinical practice. Cell therapy to release antinociceptive agents near the injured spinal cord would be the logical next step in the development of treatment modalities. But few clinical trials, especially for chronic pain, have tested the transplant of cells or a cell line to treat human disease. The history of the research and development of useful cell-transplant-based approaches offers an understanding of the advantages and problems associated with these technologies, but as an adjuvant or replacement for current pharmacological treatments, cell therapy is a likely near future clinical tool for improved health care