A geometrical approach to the motion planning problem for a submerged rigid body

The main focus of this paper is the motion planning problem for a deeply submerged rigid body. The equations of motion are formulated and presented by use of the framework of differential geometry and these equations incorporate external dissipative and restoring forces. We consider a kinematic reduction of the affine connection control system for the rigid body submerged in an ideal fluid, and present an extension of this reduction to the forced affine connection control system for the rigid body submerged in a viscous fluid. The motion planning strategy is based on kinematic motions; the integral curves of rank one kinematic reductions. This method is of particular interest to autonomous underwater vehicles which can not directly control all six degrees of freedom (such as torpedo shaped AUVs) or in case of actuator failure (i.e., under-actuated scenario). A practical example is included to illustrate our technique

EFFECTS OF THE BENCH SHIRT ON SELECTED BENCH PRESS MECHANICS

Power lifting is an individual sport enjoyed by participants in over 78 countries. Participants compete in three separate lifts and the Iifter with the highest total is the winner. However. this study is concerned purely with the bench press. The "bench shirt" is a cotton/polyester. single-ply form-fitting shirt that is used by lifters to enhance performance during the bench press. Power lifters use these shirts in an attempt to Increase the load lifted in competition. However, it Is possible that these shirts, due to their extreme form fit to the body, could alter the natural motion of the bench press exercise. Researchers have investigated the mechanics of the bench press. and identified proper technique (Judge, 1998; Madsen & McLaughlin, 1984). Proper mechanics dictate that for any experienced lifter there exists a consistent order of bar velocity (increasing velocity off of the chest, decreasing velocity throug the "sticking region," increasing velocity after the sticking region. final decreasing velocity at the finish) (Madsen & McLaughlin, 1984). The bar path should be as indicated in Figure 1. However, no published studies have demonstrated the effect the bench shirt on bench press lifting technique. Therefore. the purpose of this study was to determine the changes in bar path and bar velocity when performing the bench press shirted versus raw (no bench shirt)

The Black Lives Matter Movement: A Systemic Crisis that Expands Crisis Response Theory

Relevance to Marketing Educators, Researchers, and/or Practitioners – In response to George Floyd’s death, a variety of organizations posted messages against racism and some began to openly support Black Lives Matter, often by name, in their corporate communication initiatives. With promises of financial commitments to uplift Black communities, calls for action, and initiatives to support internal change—large and small companies, non-profits and universities—could be perceived as courageous for establishing new protocols to support such a warranted change. However, in the era of “woke washing,” or inauthentic social justice messaging, the need to assess the authenticity of corporate statements of support to social justice causes has become increasingly imperative to support both social justice causes and corporate outcomes

Surface Fuel Loadings in Mulching Treatments in Colorado Coniferous Forests

Recent large-scale, severe wildfires in the western United States have prompted extensive fuel treatment programs to reduce potential wildfire size and severity. Often, unmerchantable material is mechanically masticated because removing the material is cost-prohibitive. Mastication treatments involve shredding, chopping, or chipping small trees and/or shrubs into small chunks and leaving the material on site. While it is obvious that mechanical treatments will increase surface fuel loads, few studies have addressed how treatments alter fuel particle size and quantity. We examined how mastication treatments alter the distribution of woody material size by comparing paired masticated and untreated sites in lodgepole pine (Pinus contorta), ponderosa pine/Douglas-fir (Pinus ponderosa/Pseudotsuga menziesii), and 3) Pinyon pine (Pinus edulis) ecosystems 2-4 years after mechanical treatment. As expected, total woody fuel loadings increased in the treated areas of each ecosystem. However, the magnitude of the total increase differed among the ecosystems (lodgepole pine \u3e ponderosa pine \u3e pinyon-juniper). Average total woody fuel loads in the untreated areas ranged between 7 to 9 Mg/ha, but increased to 29 to 50 Mg/ha in treated areas. Large diameter fuels (\u3e7.62 cm) represent about 33 to 65% of the total woody fuel load in the untreated areas, but only about 11% of the total fuel load in the treated areas. The majority of woody fuels in treated areas were \u3c2.54 cm in diameter. Needle litter mass was similar among treatments, indicating that needles are still a component of the forest floor complex, but are mixed with other fuel types or buried. The increased surface woody fuel component in treated areas corresponds to a shift from a needle fuel bed to a compact woody/needle fuel bed. This change in the fuel bed composition and orientation will likely influence fire behavior and effects

Sum of squares lower bounds for refuting any CSP

Let $P:\{0,1\}^k \to \{0,1\}$ be a nontrivial $k$-ary predicate. Consider a random instance of the constraint satisfaction problem $\mathrm{CSP}(P)$ on $n$ variables with $\Delta n$ constraints, each being $P$ applied to $k$ randomly chosen literals. Provided the constraint density satisfies $\Delta \gg 1$, such an instance is unsatisfiable with high probability. The \emph{refutation} problem is to efficiently find a proof of unsatisfiability. We show that whenever the predicate $P$ supports a $t$-\emph{wise uniform} probability distribution on its satisfying assignments, the sum of squares (SOS) algorithm of degree $d = \Theta(\frac{n}{\Delta^{2/(t-1)} \log \Delta})$ (which runs in time $n^{O(d)}$) \emph{cannot} refute a random instance of $\mathrm{CSP}(P)$. In particular, the polynomial-time SOS algorithm requires $\widetilde{\Omega}(n^{(t+1)/2})$ constraints to refute random instances of CSP$(P)$ when $P$ supports a $t$-wise uniform distribution on its satisfying assignments. Together with recent work of Lee et al. [LRS15], our result also implies that \emph{any} polynomial-size semidefinite programming relaxation for refutation requires at least $\widetilde{\Omega}(n^{(t+1)/2})$ constraints. Our results (which also extend with no change to CSPs over larger alphabets) subsume all previously known lower bounds for semialgebraic refutation of random CSPs. For every constraint predicate~$P$, they give a three-way hardness tradeoff between the density of constraints, the SOS degree (hence running time), and the strength of the refutation. By recent algorithmic results of Allen et al. [AOW15] and Raghavendra et al. [RRS16], this full three-way tradeoff is \emph{tight}, up to lower-order factors.Comment: 39 pages, 1 figur