Mohd Faizan

CHARACTERIZATION OF CONTINUOUS DISTRIBUTIONS THROUGH RECORD STATISTICS

Abstract. A family of continuous probability distribution has been char-acterized through the difference of two conditional expectations, condi-tioned on a non-adjacent record statistic. Also, a result based on theunconditional expectation and a conditional expectation is used to char-acterize a family of distributions. Further, some of its deductions are alsodiscussed. 1. IntroductionLet ( X n ,n ≥ 1) be a sequence of independent, identically distributed contin-uous random variables with the distribution function ( df ) F ( x ) and the prob-ability density function ( pdf ) f ( x ). Let X u ( s ) be the s -th upper record value.Then the conditional pdf of X u ( s ) given X u ( r ) = x, 1 ≤ r 0 ,n ≥ m + 1 if and only if the distributionis exponential. Further, Lee et al. ([4]) have extended it and showed that

DFT and TD-DFT computation of charge transfer complex between o-phenylenediamine and 3,5-dinitrosalicylic acid

DFT and TD-DFT studies of o-phenylenediamine (PDA), 3,5-dinitrosalicylic acid (DNSA) and their charge transfer complex have been carried out at B3LYP/6-311G(d,p) level of theory. Molecular geometry and various other molecular properties like natural atomic charges, ionization potential, electron affinity, band gap, natural bond orbital (NBO) and frontier molecular analysis have been presented at same level of theory. Frontier molecular orbital and natural bond orbital analysis show the charge delocalization from PDA to DNSA.

Vibrational and electronic spectral analysis of 2,3-pyrazinedicarboxylic acid: A combined experimental and theoretical study

ABSTRACT Fourier transform infrared and Raman spectra of 2,3-pyrazinedicarboxylic acid were recorded and analyzed using density functional theory. The complete assignments of the anharmonic vibrational modes have been performed based on potential energy distribution. The anharmonic frequencies were computed using vibrational second-order perturbation theory as well as vibrational self-consistent field and correlation corrected vibrational self-consistent field methods. Mode–mode coupling strength is also estimated using two-mode representation of quartic force field approximation. The intra- and intermolecular interactions were also studied in the dimer and trimer forms of the title molecule. The ultraviolet–visible absorption spectra in ethanol, methanol, and acetonitrile solvents were recorded and analyzed using time-dependent density functional theory involving the polarization continuum model. The observed and calculated results are well comparable. Molecular electrostatic potential and the highest occupied and the lowest unoccupied molecular orbital analyses are also reported.

Anharmonic vibrational spectra and mode-mode couplings analysis of 2-aminopyridine

Vibrational spectra of 2-aminopyridine (2AP) have been analyzed using the vibrational self-consistence field theory (VSCF), correlated corrected vibrational self-consistence field theory (CC-VSCF) and vibrational perturbation theory (VPT2) at B3LYP/6-311G(d,p) framework. The mode-mode couplings affect the vibrational frequencies and intensities. The coupling integrals between pairs of normal modes have been obtained on the basis of quartic force field (2MR-QFF) approximation. The overtone and combination bands are also assigned in the FTIR spectrum with the help of anharmonic calculation at VPT2 method. A statistical analysis of deviations shows that estimated anharmonic frequencies are closer to the experiment over harmonic approximation. Furthermore, the anharmonic correction has also been carried out for the dimeric structure of 2AP. The fundamental vibration bands have been assigned on the basis of potential energy distribution (PED) and visual look over the animated modes. Other important molecular properties such as frontier molecular orbitals and molecular electrostatics potential mapping have also been analyzed.

Femoral artery pseudoaneurysm following trivial trauma: a rare case scenario

Pseudoaneurysm (PSA) formation in femoral artery is rare; the most common cause being arterial catheterization or penetrating trauma. Though the overall incidence of femoral artery pseudoaneurysm (FAP) following catheterization procedures is low, due to increase in number of invasive cardiovascular procedures, FAP is presented as a frequent problem. FAP can present a new thrill or bruit, pulsatile hematoma, or marked pain or tenderness. We have described a rare case report of a patient who developed a femoral artery pseudoaneurysm (FAP) following trivial trauma. In our knowledge, this is the first case report of trivial trauma leading to FAP formation. Doppler flow imaging is the mainstay of diagnosis. However, in certain cases, computed tomographic angiography is needed to plan treatment. Therapeutic options for femoral pseudoaneurysm range from observation, ultrasound-guided compression repair (UGCR), ultrasound-guided thrombin injection (UGTI), coil embolization, and endovascular repair using stent grafts to open surgical repair.

Anharmonic vibrational spectroscopy, NBO charges and global chemical reactivity studies on the charge transfer PDCA−.AHMP+ single crystal using DFT calculations

The charge transfer (CT) complex of the 2-amino-4-hydroxy-6-methylpyrimidine and 2,3 pyrazinedicarboxylic acid (PDCA-.AHMP+) was synthesized and its single crystal was grown by solution method. The structure of the crystalline complex has been investigated by single crystal X-ray diffraction (SCXRD). The vibrational features of the complex have been studied with the help of FTIR spectra and DFT computation. The anharmonic corrections in vibrational frequencies are made using the GVPT2 method at B3LYP/6-311++G(d,p) level of theory. The frontier molecular orbitals and global chemical reactivity have been calculated to understand the pharmacological aspect of the synthesized crystal. Furthermore, Hirshfeld electrostatic potential (ESP) surface, void space in the crystal structure and natural as well as Mulliken atomic charges are studied.

Nature and potency interactions of the hydrogen bond through the NBO analysis for charge transfer complex between 2-amino-4-hydroxy-6-methylpyrimidine and 2,3-pyrazinedicarboxylic acid

The intermolecular interactions in complex formation between 2-amino-4-hydroxy-6-methylpyrimidine (AHMP) and 2,3-pyrazinedicarboxylicacid (PDCA) have been explored using density functional theory calculations. The isolated 1:1 molecular geometry of proton transfer (PT) complex between AHMP and PDCA has been optimized on a counterpoise corrected potential energy surface (PES) at DFT-B3LYP/6-31G(d,p) level of theory in the gaseous phase. Further, the formation of hydrogen bonded charge transfer (HBCT) complex between PDCA and AHMP has been also discussed. PT energy barrier between two extremes is calculated using potential energy surface (PES) scan by varying bond length. The intermolecular interactions have been analyzed from theoretical perspective of natural bond orbital (NBO) analysis. In addition, the interaction energy between molecular fragments involved in the complex formation has been also computed by counterpoise procedure at same level of theory.The intermolecular interactions in complex formation between 2-amino-4-hydroxy-6-methylpyrimidine (AHMP) and 2,3-pyrazinedicarboxylicacid (PDCA) have been explored using density functional theory calculations. The isolated 1:1 molecular geometry of proton transfer (PT) complex between AHMP and PDCA has been optimized on a counterpoise corrected potential energy surface (PES) at DFT-B3LYP/6-31G(d,p) level of theory in the gaseous phase. Further, the formation of hydrogen bonded charge transfer (HBCT) complex between PDCA and AHMP has been also discussed. PT energy barrier between two extremes is calculated using potential energy surface (PES) scan by varying bond length. The intermolecular interactions have been analyzed from theoretical perspective of natural bond orbital (NBO) analysis. In addition, the interaction energy between molecular fragments involved in the complex formation has been also computed by counterpoise procedure at same level of theory.

Congenital Type I (Ia and Ib) and Type II intercalary longitudinal tibial hemimelia: A report of four cases

Congenital longitudinal tibial hemimelia is a rare disorder of lower limbs. This disorder is usually associated with skeletal and extraskeletal congenital malformation. The treatment depends on the type of tibial hemimelia. Multiple reconstructive surgeries and the availability of suitable prosthesis have an important role in treatment options. Here, we are reporting two cases of bilateral congenital Type I, one case of unilateral Type I, and one case of bilateral Type II intercalary longitudinal tibial hemimelia with one of them also had associated bilateral lobster claw hand.

Anharmonic vibrational spectral analysis of L-(-)-xylose molecule

In this work, a detailed vibrational analysis of L-(-)-xylose molecule has been carried out. The geometrical parameters and anharmonic spectrum have been calculated and compared with XRD, FTIR (4000–400cm−1) and FT-Raman (4000–50cm−1) observed data. The simulated data along with IR and Raman intensities were calculated using DFT/B3LYP level of theory in combination with 6-311++G(d,p) basis set. The experimental and theoretical results are found to be in a good agreement with each other. Moreover, thermodynamic properties, molecular electrostatic potential (MEP) and natural bond orbital (NBO) analysis of L-(-)-xylose are also reported. The calculated HOMO and LUMO energies confirm the charge transfer within the molecule.

Functional outcome of cemented bipolar prosthesis in unstable trochanteric fractures in elderly

Background Hip arthroplasty in unstable trochanteric fracture warrants quick recovery with little risk of mechanical failure, avoids the risk associated with internal fixation, and enables the patient to maintain a good level of function immediately after surgery. Aim The aim of this study is to evaluate the clinical and functional outcomes of cemented bipolar prosthesis in unstable intertrochanteric fractures in the elderly. Patients and methods Twenty-four patients with unstable type of intertrochanteric fracture according to Association Osteosynthesis Classification were treated with hemiarthroplasty (cemented bipolar prosthesis) and reconstruction of trochanter. The average age of the patients was 79 years. We evaluated postoperative complications, mortality rate, functional outcome using the Harris hip score, time to return to preinjury level of activity, and radiological signs of healing and loosening or migration of implant. The range of period of follow-up was 2–5 years (mean: 3.5 years). Results Mobilization and full weight-bearing was started immediately within 1 week of surgery. The dislocation rate in our study was zero. Deep infection and loosening of the implant was not observed in any of the cases. The mean Harris hip score improved progressively with time of follow-up. The mean score was 45.30 on the third day. The final average Harris hip score at the last follow-up was 81.90. Limb length discrepancy was observed in seven patients and average shortening was 1.3 cm (range: 0.5–1.8 cm). Conclusion Hip arthroplasty in mobile and psychologically stable elderly patients with unstable intertrochanteric fracture is a valuable treatment option.