Fractal Markets Hypothesis and the Global Financial Crisis: Scaling, Investment Horizons and Liquidity

We investigate whether fractal markets hypothesis and its focus on liquidity and invest- ment horizons give reasonable predictions about dynamics of the financial markets during the turbulences such as the Global Financial Crisis of late 2000s. Compared to the mainstream efficient markets hypothesis, fractal markets hypothesis considers financial markets as com- plex systems consisting of many heterogenous agents, which are distinguishable mainly with respect to their investment horizon. In the paper, several novel measures of trading activity at different investment horizons are introduced through scaling of variance of the underlying processes. On the three most liquid US indices - DJI, NASDAQ and S&P500 - we show that predictions of fractal markets hypothesis actually fit the observed behavior quite well.Comment: 11 pages, 3 figure

Fermion Zero Modes in Odd Dimensions

We study the zero modes of the Abelian Dirac operator in any odd dimension. We use the stereographic projection between a $(2n-1)$ dimensional space and a $(2n-1)$ sphere embedded in a $2n$ dimensional space. It is shown that the Dirac operator with a gauge field of uniform field strengths in $S^{2n-1}$ has symmetries of SU($n$)$\times$U(1) which is a subgroup of SO($2n$). Using group representation theory, we obtain the number of fermion zero modes, as well as their explicit forms, in a simple way.Comment: 14 page

Traveler Gun Irrigation of Field Grown Nursery Stock

The objective of this study was to determine annual irrigation costs for field-grown plants in Ohio by species of plant and size of firm. This objective was accomplished by synthesizing two model field nurseries using an economic engineering approach. Once the nurseries were simulated, growing space was divided into five equal parts with each segment being assigned a plant group. In the 50-acre nursery each group was allocated 8 acres of field production plus corresponding space in the propagation house, overwintering facility, holding area, and field bed area. In the 200-acre nursery each plant group was allocated 35 acres, plus corresponding space in the central facility. In each plant group, one specific species was chosen as representative for the group. Total costs of installing irrigation systems were estimated at about $82,500 for a 50-acre field nursery and$167,800 for a 200-acre field nursery. Total annual costs for irrigating the 50-acre nursery were $15,095. Irrigation costs per salable plant (represents the total costs of irrigating the plant from the time it is placed in the field bed as a liner until sale) were$0.73 for slow growing evergreens (Taxus), $0.52 for fast growing evergreens (Juniperus),$0.49 for deciduous shrubs (Viburnum), $1.62 for shade trees (Acer rubrum),$1.11 for ornamental trees (Malus), and averaged $0.73 for all species, In the 50-acre nursery, costs of irrigation were approximately 3.3$35,355. Per salable plant costs were $0.39 for slow growing evergreens (Taxus),$0.28 for fast growing evergreens (Juniperus), $0.26 for deciduous shrubs (Viburnum),$0.86 for shade trees (Acer rubrum), $0.59 for ornamental trees (Malus), and averaged$0.39 for all species. Costs of irrigation were about 2.9% of total annual costs for the 200-acre nursery. Costs of irrigation averaged approximately 87% higher per salable plant in the 50-acre nursery than in the 200-acre. Large-size commercial field nurseries use equipment and labor more efficiently than small-sized nurseries. As a result, large nurseries have a lower cost of irrigation per salable plant

Costs of Producing Field Ornamental Trees in Ohio

The objective of this study was to determine annual production costs for field-grown ornamental trees in Ohio in firms of two sizes. This objective was accomplished by synthesizing two model field nurseries using an economic engineering approach. Once the nurseries were simulated, growing space was divided into five equal parts with each segment being assigned a plant group. In the 50-acre nursery, ornamental trees were allocated 8 acres of growing space and in the 200-acre nursery 35 acres. One species of ornamental tree (Malus) was chosen for detailed analysis

Costs of Producing Shade Trees (Acer Rubrum) in the Field Differentiated by Size of Firm in Ohio

The objective of this study was to determine annual production costs for field-grown shade trees in Ohio differentiated by size of firm. This objective was accomplished by synthesizing two model field nurseries using the conceptual framework of economic engineering. Once the nurseries were synthesized, growing space was divided into five equal parts with each part being assigned a plant group. In the 50-acre nursery, slow-growing evergreens were allocated 8 acres of growing space and in the 200-acre nursery 35 acres. One specific species of shade tree (Acer rubrum) was chosen for detailed analysis