Limits on the cosmological abundance of supermassive compact objects from a search for multiple imaging in compact radio sources

Using very long baseline interferometry we have searched a sample of 300 compact radio sources for examples of multiple imaging produced by gravitational lensing; no multiple images were found with separations in the angular range 1.5--50 milliarcsec. This null result allows us to place a limit on the cosmological abundance of intergalactic supermassive compact objects in the mass range approximately 10(6)M( middle dot in circle) to approximately 10(8)M( middle dot in circle); such objects cannot make up more than approximately 1% of the closure density ( 95% confidence). A uniformly distributed population of supermassive black holes forming soon after the big bang does not, therefore, contribute significantly to the dark matter content of the Universe.     

Visual spatial memory is enhanced in female rats (but inhibited in males) by dietary soy phytoestrogens

Background  

In learning and memory tasks, requiring visual spatial memory (VSM), males exhibit superior performance to females (a difference attributed to the hormonal influence of estrogen). This study examined the influence of phytoestrogens (estrogen-like plant compounds) on VSM, utilizing radial arm-maze methods to examine varying aspects of memory. Additionally, brain phytoestrogen, calbindin (CALB), and cyclooxygenase-2 (COX-2) levels were determined.     

3D high-resolution acoustic imaging of the sub-seabed

Chirp sub-bottom profilers are marine acoustic devices that use a known and repeatable frequency-modulated source signature to produce vertical seismic reflection cross-sections of the sub-seabed. Here a 3D Chirp system is described that operates in the frequency range of 1.5-13 kHz, to produce a three-dimensional image of the sub-seabed, with typical penetration of 10-30 m and decimetric horizontal and vertical resolution. The system design incorporates a rigid frame that contains the Chirp source array together with 60 receiver elements, with positioning provided by an integrated real-time-kinematic (RTK) global positioning system (GPS). The system can be surface towed from a small survey vessel and can be applied to targets of marine geological, engineering, archaeological and defence interest. Data acquisition and processing are described for a case study which images a buried engineering structure in the Port of Southampton.     

The application of homotopy analysis method to solve nonlinear differential equation governing Jeffery–Hamel flow

In this paper Jeffery–Hamel flow has been studied and its nonlinear ordinary differential equation has been solved through homotopy analysis method (HAM). The obtained solution in comparison with the numerical ones represents a remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region.     

Neuromodulation by soy diets or equol: Anti-depressive &; anti-obesity-like influences,age- &; hormone-dependent effects

Background  

Soy-derived isoflavones potentially protect against obesity and depression. In five different studies we examined the influence of soy-containing diets or equol injections on depression, serotonin levels, body weight gain (BW) and white adipose tissue (WAT) deposition in female Long-Evans rats at various stages of life [rats were intact, ovariectomized or experienced natural ovarian failure (NOF)].     

Three-dimensional high-resolution acoustic imaging of the sub-seabed

Chirp sub-bottom profilers are marine acoustic devices that use a known and repeatable frequency-modulated source signature to produce vertical seismic reflection cross-sections of the sub-seabed. Here a 3D Chirp system is described that operates in the frequency range of 1.5-13 kHz, to produce a three-dimensional image of the sub-seabed, with typical penetration of 10-30 m and decimetric horizontal and vertical resolution. The system design incorporates a rigid frame that contains the Chirp source array together with 60 receiver elements, with positioning provided by an integrated real-time-kinematic (RTK) global positioning system (GPS). The system can be surface towed from a small survey vessel and can be applied to targets of marine geological, engineering, archaeological and defence interest. Data acquisition and processing are described for a case study which images a buried engineering structure in the Port of Southampton.     

Partitioning Infinite-Dimensional Spaces for Generalized Riemann Integration

To form Riemann sums for generalized Riemann integrals, thedomain of integration must be partitioned in a suitable manner.The existence of the required partitions is usually proved bya simple method of repeated bisection of the domain of integration.However, when the domain is the Cartesian product of infinitelymany copies of the set of real numbers, this simple method ofproof has frequently failed. A proof which works for infinite-dimensionalspaces is provided here. 2000 Mathematics Subject Classification28C20.     

Integration by parts

Many theorems of integration theory are true for a wide range of definitions of integrals. One such theorem is that giving integration by parts, and we discuss it in this paper.