Sufficient conditions for unique global solutions in optimal control of semilinear equations with C1−C^1-nonlinearity

We consider a $C^1-$semilinear elliptic optimal control problem possibly subject to control and/or state constraints. Generalizing previous work we provide a condition which guarantees that a solution of the necessary first order conditions is a global minimum. A similiar result also holds at the discrete level where the corresponding condition can be evaluated explicitly. Our investigations are motivated by G\"unter Leugering, who raised the question whether our previous results can be extended to the nonlinearity $\phi(s)=s|s|$. We develop a corresponding analysis and present several numerical test examples demonstrating its usefulness in practice

O(αs)O(\alpha_s) Corrections to B→Xse+e−B \to X_s e^+ e^- Decay in the 2HDM

$O(\alpha_s)$ QCD corrections to the inclusive $B \to X_s e^+ e^-$ decay are investigated within the two - Higgs doublet extension of the standard model (2HDM). The analysis is performed in the so - called off-resonance region; the dependence of the obtained results on the choice of the renormalization scale is examined in details. It is shown that $O(\alpha_s)$ corrections can suppress the $B \to X_s e^+ e^-$ decay width up to $1.5 \div 3$ times (depending on the choice of the dilepton invariant mass $s$ and the low - energy scale $\mu$). As a result, in the experimentally allowed range of the parameters space, the relations between the $B \to X_s e^+ e^-$ branching ratio and the new physics parameters are strongly affected. It is found also that though the renormalization scale dependence of the $B \to X_s e^+ e^-$ branching is significantly reduced, higher order effects in the perturbation theory can still be nonnegligible.Comment: 16 pages, latex, including 6 figures and 3 table

Throughput Scaling Laws for Wireless Networks with Fading Channels

A network of n communication links, operating over a shared wireless channel, is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. It is assumed that each link can be active and transmit with a constant power P or remain silent. The objective is to maximize the throughput over the selection of active links. By deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading (i) the maximum throughput scales like $\log n$ (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links by a chi-squared random variable. To obtain the lower bound, a decentralized link activation strategy is proposed and analyzed.Comment: Submitted to IEEE Transactions on Information Theory (Revised

Morbidity Pattern Among Out-Patients Attending Urban Health Training Centre in Srinagar

The current study was designed to identify the morbidity pattern of out-patients attending Urban Health Training Centre in an urban area of a medical college in Srinagar, Pauri Garhwal district, Uttarakhand, North India. The present study record-based retrospective study was conducted among the out-patients attending the regular clinic at the Urban Health Training Centre, of a medical college in Srinagar city of Uttarakhand State of North India during the study period of one year in 2014. Data was retrieved from the OPD registers maintained at the clinic. Data was collected pertaining to socio-demographic profile, morbidity details and treatment pattern. Diseases were identified using the International Classification of Diseases (ICD-10) code. Descriptive analysis was done. During the study period, a total of 9343 subjects attended the OPD. Among them, majority of them (60%) were females. More than half (56 %) belonged to the age group of 35-65 year age-group. The association of disease classification was found to be statistically significant with respect to gender. The leading morbidity of communicable disease was found to be certain infectious and parasitic diseases especially Typhoid whereas musculoskeletal system and connective tissue disorders were the most common cause among morbidity due to NCDs. Out of all, typhoid was found to cause maximum of morbidity among the subjects. The present study highlights the morbidity pattern of communicable and NCDs among the population of hilly areas of Garhwal, Uttarakhand India. Priority should be preferred for the regular tracking of diseases in terms of preventive and promotive aspects. Morbidity in the out- door clinics reflects the emerging trend of mixed disease spectrum burden comprising communicable and non-communicable diseases