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In this paper we have considered the following coupled system of nonlinear ordinary differential equations. x n 1 1 (t)=f 1 (t,x 2 (t))

In this paper we deal with the Nonlinear Coupled Ordinary Dif- ferential Equations(Nonlinear CODE). A Multipoint Boundary Value Prob- lem(MBVP) associated with these Nonlinear Equations is deflned as an Oper- ator Equation. This equation(inflnite dimensional) is reduced to an Equivalent Bifurcation Equation(flnite dimensional) using Schauder's Fixed Point Theo- rem. This Bifurcation Equation being on a flnite dimensional space can be easily solved by using standard approximation techniques.

A 47-year-old man presented with a history of oliguria and uraemic symptoms such as anorexia, nausea and vomiting. His serum creatinine on admission was 8.5 mg/dl and his arterial blood gas revealed metabolic acidosis. He was enrolled for regular sessions of haemodialysis following which his symptoms improved remarkably and his serum creatinine returned to normal. A renal biopsy done at this time showed a moderate tubulo-interstitial nephritis with mild global glomerular sclerosis. The patient returned 1 month later with severe back ache and a computed tomography (CT) scan of the lumbosacral spine was undertaken …

The aim of this case series is to evaluate the pattern of breast lumps in males and females with special reference to spectrum of lesions in females below 40 years of age. A 20 years retrospective study was undertaken from the records of the department of Pathology, Bhopal. The lesions were classified into benign and malignant. In young females histological pattern was analyzed in various age groups. A total of 1824 cases were studied. 1724 (94.5%) cases were seen in females and 100 (5.5%) in males. There were 1276 (74%) females below 40 years of age and 448 (26%) were above 40 years of age. In young females 1136 (89%) lesions were benign and 140 (11%) were malignant lumps. Fibrocystic disease in 60 (49%) cases constituted the largest group of benign lumps followed by 30 (24.5%) cases of inflammatory lesion in older females. The mean age of malignant tumors was 34.1 in young females and 51.4 in females above 40. Infiltrating duct carcinoma constituted 83.5% of malignant tumors in young females and 86.1% in older females.

Choristoma is defined as a histologically normal tissue proliferation or nodule of a tissue type not normally found in anatomic site of proliferation. Here a case of chronic tonsillitis is being reported where mature cartilage was found embedded in the tonsil, making the surgical removal of the tonsil difficult. Cartilaginous choristoma of the tonsil appears to be a developmental anomaly in the second pharyngeal arch and could be one of the causes of recurrent tonsillitis.

Functional sternomastoid myoplasty is a surgical procedure for the correction of congenital torticollis. It allows increment in muscle length without disrupting its bony attachments, hence preserving its function. The technique and rationale of the procedure are discussed.Observations in six patients indicate that the best functional and cosmetic results can be realized when surgery is performed during childhood.

Inelastic and elastic J/psi photoproduction on hydrogen are investigated at a mean energy of 105 GeV. The inelastic cross section with E/sub psi/ /E/sub ..gamma../

We have studied muon-produced hadrons from a deuterium target. The structure functions and the charge ratios are reported for neutrons; the transverse momentum and azimuthal distributions are reported for deuterons. The structure function for the neutron is similar to that of the proton. The charge ratio of produced hadrons follows the expectation of a simple spin-1/2 quark model. Transverse-momentum results agree with those at lower energy and are similar to those from hadron--hadron interactions. No azimuthal anisotropy is seen. (AIP)

We have studied D( production mechanisms using data from a photoproduction experiment at the Fermilab Tagged Photon Spectrometer. A large sample of charged D('s was selected via the clean signature of the cascade decay D(..-->..D/sup 0/..pi../sup +/ and subsequently D/sup 0/..-->..K/sup -/..pi../sup +/ or D/sup 0/..-->..K/sup -/..pi../sup +/..pi../sup 0/. The cross section for the process ..gamma..p..-->..(D/sup asterisk+/+anything)p at an average energy of 105 GeV was measured to be 88 +- 32 nb. Only (11 +- 7)% of D('s were found to be consistent with being accompanied solely by a D-bar( or a D-bar; the remaining events contain additional particles. The distribution of the production angle of the D( in the photon-fragmentation-system center of mass is strongly anisotropic and consistent with the form f(theta() = cos/sup 4/theta(. We set a limit on the associated-production-process cross section sigma(..gamma..p..-->..(D-bar/sup asterisk-/+anything)..lambda../sub c/)

Inclusive hadron production in muon-proton inelastic scattering has been measured for ${q}^{2}g0.5$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ and $10l\ensuremath{\nu}l135$ GeV. The results are presented in the form of the transverse momentum distribution of charged hadrons and the hadron invariant structure function $F({x}^{\ensuremath{'}})$. Results are given for different regions of ${q}^{2}$ and $s$.

A 59-layer lead-liquid scintillator shower detector has been tested in an electron beam at SLAC. The energy resolution is about 9%/√E. The detector is optically segmented into counters by means of thin, teflon-coated, bent aluminum panels. The position of the shower is determined to a precision of a few mm by comparing the relative sizes of the signals from neighboring counters.

This paper reports measurements of the hadrons produced in the inelastic scattering of 147-GeV muons by protons and deuterons in an experiment carried out at Fermi National Accelerator Laboratory. Both the scattered muon and the hadrons were measured in a large spectrometer. Properties of the hadron spectra are presented for proton, deuteron, and neutron targets and compared with theoretical models and with hadron spectra from related processes. Emphasis is placed on the quark-parton model and the data are found to be in substantial agreement with it. The average transverse momentum of the hadrons with respect to the virtual photon direction shows no dependence on the muon scattering variables. The data display "jet behavior" of the inclusive hadrons comparable to that found in ${e}^{+}{e}^{\ensuremath{-}}$ annihilations.

We have studied the production of $\ensuremath{\rho}$ and $\ensuremath{\varphi}$ mesons from muon scattering on a liquidhydrogen target at 150 and 100 GeV. For the $\ensuremath{\rho}$ we observe a skewed mass distribution which becomes somewhat more normal with increasing ${Q}^{2}$ (the square of the four-momentum transferred from the muon), and an exponential distribution in $t$ (the square of the four-momentum transferred to the target proton) with a slope which is consistent with a slight decrease as ${Q}^{2}$ increases. The dependence of the cross section on ${Q}^{2}$ follows that of the square of the $\ensuremath{\rho}$ propagator with little contribution from longitudinal $\ensuremath{\rho}$ production. The angular distribution of the $\ensuremath{\rho}$ decay confirms the smallness of the contribution from longitudinal $\ensuremath{\rho}$ production at our energies. The cross section when extrapolated to ${Q}^{2}=0$ agrees with that measured in real photoproduction. The decay angular distribution of the $\ensuremath{\rho}$ decay shows that $s$-channel helicity is largely conserved, although we detect a helicity-single-flip contribution at the 10-15% level. Natural-parity exchange in the $t$ channel dominates, and the transverse and longitudinal amplitudes are found to be in phase. These characteristics are consistent with the diffractive nature of the vectordominance model. The $t$ distribution of $\ensuremath{\varphi}$ production is also exponential, although less steep than that for the $\ensuremath{\rho}$. We observe an elastically produced four-pion state at a mass of approximately 1600 MeV. We identify this state with the ${\ensuremath{\rho}}^{\ensuremath{'}}(1600)$, and find it to be produced with a distribution exponential in $t$.

Results are presented from an experiment observing photoproduction of the D( at a mean energy of 105 GeV. Clean signals are seen for the decay D/sup asteriskplus-or-minus/..--> pi../sup + -/D/sup 0/ with the D/sup 0/ decaying into both K/sup - +/..pi../sup + -/ and K/sup - +/..pi../sup + -/..pi../sup 0/. Analysis of the Dalitz plot for the k..pi pi.. mode gives branching fractions for K/sup -/rho/sup +/, K/sup asterisk-/..pi../sup +/, and K-bar /sup asterisk0/..pi../sup 0/ final states.

Results on the nucleon structure function, $\ensuremath{\nu}{W}_{2}$, are presented for $0.2l~{q}^{2}l~50$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ and $5l~\ensuremath{\nu}l~130$ GeV. They were obtained by scattering 147-GeV positive muons inelastically from a liquid deuterium target.

Measurements have been made of the inclusive scattering of 96, 147, and 219 GeV muons from hydrogen, and of 147 GeV muons from deuterium. Results are presented for the nucleon structure function F/sub 2/(x,Q/sup 2/) (equivalent..nu..W/sub 2/(x,Q/sup 2/)) for 10 < ..nu.. < 200 GeV and 0.2 < Q/sup 2/ < 80 GeV/sup 2/. The value of F/sub 2/ rises with Q/sup 2/ at small x, and falls with Q/sup 2/ at large x, in agreement with the ideas of quantum chromodynamics. An average value of the ratio sigma/sub L//sigma/sub T/ equivalent R = 0.52 +- 0.35 has been obtained for the region 0.003 < x < 0.10 and 0.4 < Q/sup 2/ < 30 GeV/sup 2/. The values of F/sub 2/ from this experiment have been combined with those from other charged-lepton scattering experiments to determine moments of the structure functions. The variation with Q/sup 2/ of these moments is used to derive values for ..lambda.., taking into account corrections up to second order in ..cap alpha../sub s/. The fit to the data is very good.

Cross sections for diffractive rho muoproduction in hydrogen are presented for 90 GeV

A 60 layer lead-liquid scintillator shower detector, which we call the SLIC, has been used for multiphoton detection in the Fermilab tagged photon spectrometer. The detector has an unimpeded active area which is 2.44 m by 4.88 m and is segmented, by means of teflon coated channels, into 3.17 cm wide strips. The 60 layers in depth are broken into three directions of alternating readouts so that three position coordinates are determined for each shower. At present the readouts are made by 334 photomultiplier tubes coupled to BBQ doped wavelength shifter bars which integrate the entire depth of the detector. It is relatively straightforward to increase the number of readouts to include longitudinal segmentation and to increase the segmentation of the outer region which are at present read out two strips to a readout. The energy and position resolutions of isolated showers are about 12%√E and 3 mm., respectively. The SLIC has been used to study the K−π+π0 decay of the D0 [1], as well as for electron and muon identification in ψ → e+e− and ψ → μ+μ− plus π0 identification in γp → ψχ [8].

Results on the proton structure function, $\ensuremath{\nu}{W}_{2}$ are presented for $0.3l{q}^{2}l50$ Ge${\mathrm{V}}^{2}$ and $5l\ensuremath{\nu}l130$ GeV. They are compared to earlier data and displayed to demonstrate violations of scaling. Values are reported for the energy-momentum sum rule and for $R\ensuremath{\equiv}\frac{{\ensuremath{\sigma}}_{L}}{{\ensuremath{\sigma}}_{T}}$ over a limited kinematic region.

Design of a 53 MHz 4 MV short duty cycle rf system for bunch rotation in the Fermilab antiproton source has been described previously. Fabrication and installation of the system has been completed. The rf cavities in the system are comletely evacuated welded aluminum structures, each capable of generating 700 kV with a very low duty factor. This report will describe fabrication procedures, multipactor inhibiting techniques, and initial operating experience with the system, Of particular interest is the capability for reduction of the rf voltage to a very small value witin 40 microseconds (25 turns) at the end of the momentum reduction, thus inhibiting further bunch rotation.

We have observed coherent production of $\ensuremath{\rho}$ mesons by muon scattering on carbon. The differential cross section falls steeply with increasing $t$ (the square of the four-momentum transferred to the nucleus) and helicity is conserved in the $s$ channel. Dominance by coherent production, as well as the radius of the carbon nucleus and the total $\ensuremath{\rho}$-nucleus cross section derived from our measurements, are consistent with what is observed in other related processes.

The hair patterns of the pinna have been studied in a selected sample of 767 males and 5 females from Central India, all with hairy pinnae. The age of the males ranged from 21 to 85 years, and that of the females from 2.5 months to 32 years. All subjects were healthy and did not demonstrate any endocrine disturbance. The commonest hair pattern of the elevated areas of the pinna among the males was the helico-lobulo-antitragal, whereas in the females it was the helical. The hair pattern of the depressed areas of the pinna showing highest frequency was the conchal. The majority of the hairy pinnae are associated with bilateral tragal hair and the maximo-pilose distribution of the facial hair. The Central Indian males resemble the White males in their hair distribution of the pinna.

Unilateral ulceration, bone necrosis, and sequestrum formation in the external auditory meatus are at times confused with the general diagnosis of keratosis obturans. However, the clinical presentation and the radiological and pathological characteristics of this condition are quite distinct from the latter. Initial examination in this situation may raise the suspicion of malignancy. When a true cholesteatoma of the external auditory meatus is found in association with this entity, according to a review of the available literature and personal observation of the authors, it is the result rather than the cause of this pathological process. In order to clarify this relationship, three patients are presented in whom there is radiological and histological evidence of bone necrosis and sequestration of a segment of the temporal bone but no evidence of hyperkeratosis in the ear canal.