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If physicalism is true, everything is physical. In other words, everything supervenes on, or is necessitated by, the physical. Accordingly, if there are logical/mathematical facts, they must be necessitated by the physical facts of the world. The aim of this paper is to clarify what logical/mathematical facts actually are and how these facts can be accommodated in a purely physical world.

Economics is a very powerful discipline that focuses on some important aspects of our life, in particular, constrained maximization equilibrium in resource allocation. However, orthodox economics based on simplified models and many economists much captured by such models have too narrow a focus, ignoring many important factors including the importance of competition for relative standing, environmental disruption, and behaviour patterns inconsistent with the narrow concept of rationality. Economics has also become excessively formalistic, sacrificing relevance for technical sophistication. Extensions of economics to overcome these weaknesses have been and are being made. The incorporation of these advances will make economics more useful. But more time and resources may be needed to train economists properly.

On the basis of the Berkovits pure spinor formalism of covariant quantization of supermembrane, we attempt to construct a M(atrix) theory which is covariant under SO(1, 10) Lorentz group. We first construct a bosonic M(atrix) theory by starting with the first-order formalism of bosonic membrane, which precisely gives us a bosonic sector of M(atrix) theory by BFSS. Next we generalize this method to the construction of M(atrix) theory of supermembranes. However, it seems to be difficult to obtain a covariant and supersymmetric M(atrix) theory from the Berkovits pure spinor formalism of supermembrane because of the matrix character of the BRST symmetry. Instead, in this paper, we construct a supersymmetric and covariant matrix model of 11D superparticle, which corresponds to a particle limit of covariant M(atrix) theory. By an explicit calculation, we show that the one-loop effective potential is trivial, thereby implying that this matrix model is a free theory at least at the one-loop level.

Four formulations of quantum mechanics on noncommutative Moyal phase spaces are reviewed. These are the canonical, path-integral, Weyl–Wigner and systematic formulations. Although all these formulations represent quantum mechanics on a phase space with the same deformed Heisenberg algebra, there are mathematical and conceptual differences which we discuss.

We study T-duality transformations in canonical formalism for Nambu–Goto action. Then we investigate the relation between worldsheet double Wick rotation and sequence of target space T-dualities and Wick rotation in case of fundamental string and D1-brane.

Using the complex Klein–Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The Lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and charge operators. Conversely to the complex case, the quaternionic quantization admits two quantization schemes, concerning either two or four components. Therefore, the quaternionic field permits a richer structure of states, if compared to the complex scalar field case. Moreover, the quaternionic theory admits as a further novel feature a non-associative algebraic structure in their complex components, something not observed in the complex case.

The second quantization of the quaternionic fermionic field is undertaken using the real Hilbert space approach to quaternionic quantum mechanics (${ℍ}$QM). The solution responds to an open problem of quaternionic quantum theory, and launches the basis to the development of the quaternionic interaction theory.

The inception of maqasid as-shari’ah al-Tawhid index of socio-economic development sustainability is presented in its generalized form. This involves a unified relational methodological formalism. The resulting model is that of wellbeing, which in Islamic context is referred to as maslaha. The maslaha function is formalized and applied to the specific case of socio-economic development sustainability. This term signifies the importance that moral and ethical values hold in a substantively participatory context of choices of the good things of life, while avoiding the harmful ones. The meaning is linked to and bears on moral, social and economic development perspectives. Sustainability of development as a participatory process yielding well-being is thereby a relational organic continuation in pervasive complementarities between endogenous and circular causation relations of critical variables under the impact of Tawhid as law inducing the variables by its ontology of unity of knowledge. A specific example of application is taken as the formulation and relational explanation of the Gender Development Index in terms of its various critical variables of wellbeing. Statistical analysis and policy conclusions are carried out.