Comeback from Failure

John 21:1-2

Efficient digital-to-analog encoding

An important issue in analog circuit design is the problem of digital-to-analog conversion, i.e., the encoding of Boolean variables into a single analog value which contains enough information to reconstruct the values of the Boolean variables. A natural question is: what is the complexity of implementing the digital-to-analog encoding function? That question was answered by Wegener (see Inform. Processing Lett., vol.60, no.1, p.49-52, 1995), who proved matching lower and upper bounds on the size of the circuit for the encoding function. In particular, it was proven that [(3n-1)/2] 2-input arithmetic gates are necessary and sufficient for implementing the encoding function of n Boolean variables. However, the proof of the upper bound is not constructive. In this paper, we present an explicit construction of a digital-to-analog encoder that is optimal in the number of 2-input arithmetic gates. In addition, we present an efficient analog-to-digital decoding algorithm. Namely, given the encoded analog value, our decoding algorithm reconstructs the original Boolean values. Our construction is suboptimal in that it uses constants of maximum size n log n bits; the nonconstructive proof uses constants of maximum size 2n+[log n] bits

Review of nondestructive testing techniques for detecting lack of penetration in aluminum fusion welds

Nondestructive testing for detecting lack of penetration in aluminum fusion weld

Turbulence and turbulent mixing in natural fluids

Turbulence and turbulent mixing in natural fluids begins with big bang turbulence powered by spinning combustible combinations of Planck particles and Planck antiparticles. Particle prograde accretions on a spinning pair releases 42% of the particle rest mass energy to produce more fuel for turbulent combustion. Negative viscous stresses and negative turbulence stresses work against gravity, extracting mass-energy and space-time from the vacuum. Turbulence mixes cooling temperatures until strong-force viscous stresses freeze out turbulent mixing patterns as the first fossil turbulence. Cosmic microwave background temperature anisotropies show big bang turbulence fossils along with fossils of weak plasma turbulence triggered as plasma photon-viscous forces permit gravitational fragmentation on supercluster to galaxy mass scales. Turbulent morphologies and viscous-turbulent lengths appear as linear gas-proto-galaxy-clusters in the Hubble ultra-deep-field at z~7. Proto-galaxies fragment into Jeans-mass-clumps of primordial-gas-planets at decoupling: the dark matter of galaxies. Shortly after the plasma to gas transition, planet-mergers produce stars that explode on overfeeding to fertilize and distribute the first life.Comment: 23 pages 12 figures, Turbulent Mixing and Beyond 2009 International Center for Theoretical Physics conference, Trieste, Italy. Revision according to Referee comments. Accepted for Physica Scripta Topical Issue to be published in 201

“The path of social justice”: A Human Rights History of Social Justice Education

Although not often recognized, social justice education in the U.S. is historically and philosophically tied to the twentieth century\u27s human rights initiatives. The efforts of human rights pioneers, such as those who authored the Universal Declaration of Human Rights, have indelibly shaped social justice efforts, including within education, in the U.S. Reframing social justice education in light of human rights gives clarity to and concretizes our work as social justice educators: It strengthens a vision of education as central to promoting rights and justice; it refocuses attention on a broader array of fundamental rights, and it explicitly contests our globalized and neoliberal context, a context heavily influencing educational reform