Abstract:
The parton content of the electron is analyzed within perturbative QCD. It is shown that electron acquires an anomalous component from QCD, analogously to photon. The evolution equations for the `exclusive' and `inclusive' electron structure function are constructed and solved numerically in the asymptotic $Q^2$ region.

Abstract:
We study the problem of existence, uniqueness and approximation of solutions of finite dimensional Stratonovich stochastic differential equations with reflecting boundary condition driven by semimartingales with jumps. As an application we generalize known results on the Wong-Zakai type approximations.

Abstract:
We study approximations of reflected It\^o diffusions on convex subsets $D$ of $\Rd$ by solutions of stochastic differential equations with penalization terms. We assume that the diffusion coefficients are merely measurable (possibly discontinuous) functions. In the case of Lipschitz continuous coefficients we give the rate of $L^p$ approximation for every $p\geq1$. We prove that if $D$ is a convex polyhedron then the rate is $O((\frac{\ln n}n)^{1/2})$, and in the general case the rate is $O((\frac{\ln n}n)^{1/4})$.

Abstract:
A novel theoretical model is presented maintaining that consciousness evolved on the basis of time distinctions. Various models of time pertain to the existence of future, present and past. It is proposed that the future represents potentialities, the present the actualization of certain potentialities, and the past a record of actualized potentialities. Actualization of potentialities derives from micro quantum wave function collapses with specific constellations corresponding to macro level form. Consciousness provides for an awareness of potentialities being actualized in the present, the time frame of consciousness closely aligning with the time frame of potentialities being actualized in the moment. Evolution of such awareness is highly probable, given the ensuing motivation enabling behavior to be altered in the moment to minimize the actualization of maladaptive potentialities, and maximize the actualization of adaptive potentialities. The model also provides a logical proof for the occurrence of time distinctions.

Abstract:
The QCD structure of the electron is defined and calculated. The leading order splitting functions are extracted, showing an important contribution from $\gamma$-$Z$ interference. Leading logarithmic QCD evolution equations are constructed and solved in the asymptotic region where log$^2$ behaviour of the parton densities is observed. Corrections to the naive evolution procedure are demonstrated. Possible applications with clear manifestation of 'resolved' photon and weak bosons are discussed.

Abstract:
The collinear QCD structure of the electron is studied within the Standard Model. The electron structure function is defined and calculated in leading logarithmic approximation. It shows important contribution from the interference of the intermediate electroweak bosons. The problem of momentum scales is extensively discussed. The master equations for the QCD parton densities inside the electron are constructed and solved numerically in the asymptotic region. Significant corrections to the naive evolution procedure are found. Phenomenological applications at present and future momentum scales are discussed.

Abstract:
The QCD structure of the electroweak bosons is reviewed and the lepton structure function is defined and calculated. The leading order splitting functions of electron into quarks are extracted, showing an important contribution from $\gamma$-$Z$ interference. Leading logarithmic QCD evolution equations are constructed and solved in the asymptotic region where log$^2$ behaviour of the parton densities is observed. Possible applications with clear manifestation of 'resolved' photon and weak bosons are discussed.

Abstract:
The influence of the QCD structure of the weak bosons on the Higgs boson production in $e$-$p$ scattering is studied. The energy and Higgs boson mass dependence of the cross-section, following from the new contributions, is calculated.

Abstract:
The electron and photon structure functions are compared. Advantages of the electron structure function are demonstrated. At very high momenta probabilistic (partonic) interpretation can be preserved despite strong $\gamma$-$Z$ interference. At present energies analyses of both the electron and the photon structure functions give an important test of the experimentally applied methods. Predictions for the electron structure function at present and future momenta are given.

Abstract:
Advantages of introducing the electron structure function (ESF) in electron induced processes are demonstrated. Contrary to the photon structure function it is directly measured in such processes. At present energies a simultaneous analysis of both the electron and the photon structure functions gives an important test of the experimentally applied methods. Estimates of the ESF at currently measured momenta are given. At very high momenta contributions from $W$ and $Z$ bosons together with $\gamma$-$Z$ interference can be observed. Predictions for next generation of experiments are given.