The superconducting circuit community has recently discovered the promising potential of superinductors. These circuit elements have a characteristic impedance exceeding the resistance quantum $R_text{Q} approx 6.45~text{k}Omega$ which leads to a sup
pression of ground state charge fluctuations. Applications include the realization of hardware protected qubits for fault tolerant quantum computing, improved coupling to small dipole moment objects and defining a new quantum metrology standard for the ampere. In this work we refute the widespread notion that superinductors can only be implemented based on kinetic inductance, i.e. using disordered superconductors or Josephson junction arrays. We present modeling, fabrication and characterization of 104 planar aluminum coil resonators with a characteristic impedance up to 30.9 $text{k}Omega$ at 5.6 GHz and a capacitance down to $leq1$ fF, with low-loss and a power handling reaching $10^8$ intra-cavity photons. Geometric superinductors are free of uncontrolled tunneling events and offer high reproducibility, linearity and the ability to couple magnetically - properties that significantly broaden the scope of future quantum circuits.
The degree pattern of a finite group is the degree sequence of its prime graph in ascending order of vertices. We say that the problem of OD-characterization is solved for a finite group if we determine the number of pairwise nonisomorphic finite gro
ups with the same order and degree pattern as the group under consideration. In this article the problem of OD-characterization is solved for some simple unitary groups. It was shown, in particular, that the simple unitary groups $U_3(q)$ and $U_4(q)$ are OD-characterizable, where $q$ is a prime power $<10^2$.
Individuals often develop reluctance to change their social relations, called secondary homebody, even though their interactions with their environment evolve with time. Some memory effect is loosely present deforcing changes. In other words, in pres
ence of memory, relations do not change easily. In order to investigate some history or memory effect on social networks, we introduce a temporal kernel function into the Heider conventional balance theory, allowing for the quality of past relations to contribute to the evolution of the system. This memory effect is shown to lead to the emergence of aged networks, thereby perfectly describing and the more so measuring the aging process of links (social relations). It is shown that such a memory does not change the dynamical attractors of the system, but does prolong the time necessary to reach the balanced states. The general trend goes toward obtaining either global (paradise or bipolar) or local (jammed) balanced states, but is profoundly affected by aged relations. The resistance of elder links against changes decelerates the evolution of the system and traps it into so named glassy states. In contrast to balance
