Stock mechanics theory of conservation of total energy and predictions of coming short-term

Stock mechanics: theory of conservation of total energy and predictions of coming short-term fluctuations of Dow Jones

Industrials Average (DJIA)

?a ?lar Tuncay

Department of Physics, Middle East Technical University

06531 Ankara, Turkey

caglart@https://www.wendangku.net/doc/b717193909.html,.tr

Abstract

Predicting absolute magnitude of fluctuations of price, even if their sign remains unknown, is important for risk analysis and for option prices. In the present work, we display our predictions about absolute magnitude of daily fluctuations of the Dow Jones Industrials Average (DJIA), utilizing the original theory of conservation of total energy, for the coming 500 days.

Introduction

One may define total energy (E T ) for prices χ(t) (taking mass equal to unity) as

E T = ? v 2 + U , (1)

where v is the usual speed, i.e., v(t)=d χ(t)/dt, and U is the potential energy. In literature a few number of references, which utilize the idea of potential energy is found [1-10]. J-P. Bouchaud, and R. Cont [1] developed a quadratic form within a Langevin approach, and in

[2], J-P. Bouchaud studied a more complex expression involving a term with power three besides a quadratic one. In [3, 4] a potential energy corresponding to some states of random motion is phrased. An angle dependent potential is utilized to describe equilibrium and off equilibrium price states in [5]. K. Ide and D. Sornette studied oscillatory finite-time singularities in finance [6, 7], where the time derivative of speed was written in terms of a linear combination of χn and v m

, with arbitrary powers (See Eqs. (11)-(13), (32), (33), in [6], and Eqs. (1)-(3) in [7].) There, no assumption about the conservation of the sum of kinetic and potential energies was made. They have obtained oscillations and up (down) trends by neglecting the speed and restoring terms, respectively. Recently, we described some aspects of potential energy for price oscillations in [8], in terms of buying and selling processes within a herding mechanism. More recently, we proposed and utilized conservation of sum of potential and kinetic energy to make some predictions on several world indices [9, 10], where a linear potential energy (U=g χ) was also proposed for the current epoch of DJIA, S&P500, and NASDAQ. The corresponding equations of motion (obtained by taking the time time derivative of Eq. (1) and equating it to zero as d 2χ(t)/dt 2 = -g, and integrating afterwards)

χ(t) = χ0 + v 0t – ? g t 2 (2)

survived as valid for the behavior of the DJIA, S&P500, and NASDAQ[8,10], within the last nine months after we proposed it, as shown for DJIA in Fig. 1. Unit for price (value) is taken as local currency unit (lcu), and for time as (day).

In the present work DJIA will be focused on, because its time domain is the longest and volume is largest of all the world indices. One may see Fig. 1. and its caption for the explicit form of Eq. (2) and the parameters therein, where (and in other related figures and computations) real data in [11] is utilized up to 30 Dec 2005.

Conservation of total energy and predicting daily fluctuations for future

As shown empirically in [10], the general trends averaged over months or years gave a roughly conserved total energy. The corresponding equation of motion for the current epoch, Eq. (2), may be decorated for future’s probable behavior of the price as

χfuture (t) = χ(t) (1 – α(0.5-δ(t)) , (4)

where χ(t) is the expression in Eq (2), and δ(t) is the random function with 0≤δ(t)<1. In Eq(4) α is any scaling factor, which controls the maximum value of deviation of the probable future value of the index from Eq. (2), where the shape remains independent of α. In reality α may also depend on the regulations of the exchange, since in some countries arbitrary fluctuations are not allowed and limited by law. α maybe taken as 0.3 for DJIA for reasonable results with ±15% daily variations (probable) at maximum. It is clear that perfection can never be reached with any prediction, yet one may try better randomization processes for better approximations. Utilizing Eq. (9) of [8], we obtained the results displayed in Figs. 2. a., b., where the initial date (i.e. the first day) is taken as 02 Jan 1998. In the upper part of Fig. 2. b., the original (one of the probable) results are displayed with a shifted vertical axis, in order to seperate the upper curve from the lower one. In the lower curve of Fig. 2. b., which involves results of the real data, fluctuations after t=1251 (day) have become smaller than they were before. For the term 1< t < 625 (day) the same effect is also present but less visible, where some fluctuations have occured with big amplitudes at a few number of days.

Summary and conclusion

With a linear potential energy for the current epoch of DJIA, energy conservation theory yields in equations of motion for the index in terms of long-term moving averages, which may be utilized by some random decoration processes for future. Then the resulting decorated index value may be used for short-term (day to day) fluctuations and for their averages. As predicted within the present formalism, the index will fall to 8,000’s and below within the coming 500 days, as a result the fluctions will increase accordingly, as shown on the right hand side bottom corner of Fig 2. a.

Acknowledgement

The author is thankful to Dietrich Stauffer for his friendly discussions and corrections, and supplying some references.

References

[1] J-P. Bouchaud and R. Cont, “A Langevin approach to stock market fluctuations and crashes”, Eur. Phys. J. B 6, 543–550 (1998). Preprint: arXiv:cond-mat/9801279.

[2] J-P. Bouchaud, “Power laws in economics and finance: some ideas from physics”, Quant. Fin. 1, 105–112 (2001). Preprint: arXiv:cond-mat/0008103.

[3] I. Chang, and D. Stauffer, “Fundamental judgement in Cont-Bouchaud Herding model of market fluctuations”, Physica A 264, 294–298 (1999).

[4] E. Frey, and K. Kroy, “Brownian motion: a paradigm of soft matter and biological physics”. Preprint: arXiv:cond-mat/0502602.

[5] J. A. Holyst, W. Wojciechowski, “The effect of Kapitza pendulum and price equilibrium” Physica A 324, 388–395 (2003).

[6] K. Ide, D. Sornette, “Oscillatory Finite-Time Singularities in Finance, Population and Rupture”, Physica A 307, 63–106 (2002). Preprint: arXiv:cond-mat/0106047.

[7] D. Sornette, K. Ide, “Theory of self-similar oscillatory finite-time singularities in Finance, Population and Rupture”, Int. J. Mod. Phys. C 14 (3), 267–275 (2002), Preprint:

arXiv:cond-mat/0106054.

[8] ?. Tuncay, “Stock mechanics: a classical approach”. Preprint: arXiv:physics/0503163.

[9] ?. Tuncay, “Stoch mechanics: predicting recession in S&P500, DJIA, and NASDAQ”, Central European Journal of Physics 4 (1), 1–15 (2006). Preprint: arXiv:physics/0506098. [10] ?. Tuncay, “Stock mechanics: a general theory and method of energy conservation with applications on DJIA”, scheduled for Int. J. Mod. Phys. C 17/ issue 6. Preprint:

arXiv:physics/0512127.

[11] For detailed information about DJIA and other NYSE indices and shares, URL:

https://www.wendangku.net/doc/b717193909.html,/i/.

Figure captions

Figure 1. DJIA, about the Apr-Sep2000 climax is described by a rise and a fall of the price in a gravity g = –0.01212 (lcu/day2). The initial (shooting) speed at the beginning of 1995 is v01= 10.17 (lcu/day). The price falls down after the maximum height and inelastically bounces back with v02= 8.43 (lcu/day) in the same gravity, and rises up to 11,000’s in accordance with the expression χ – χ0= (v0)2/2g, which is obtained by taking time derivative of Eq. (1) and equating it to zero and performing a few algebraic opererations afterwards. A recession, back to 8,000’s and below is expected within the coming 500 days.

Figure 2.Excel graphics for the probable future fluctuations of DJIA, which are obtained in terms of Eq. (9) of [8].

Figure 2. a.Probable decoration of the index for the past (from 02 Jan 1998 up to

30 Dec 2005, covering 2001 days) and for the coming 500 days. The inset

below involves , where the amplitude depends on α of Eq. (4). Thin line

is the index, dashed line is the equation of motion for a linear -gravitational-

potential energy of Eq. (3), and thick line is the decoration involving

randomness of Eq. (4).

Figure 2. b. Probable fluctuations of returns due to decoration displayed in Fig. 2. a.

The vertical axis is shifted to 1000 delibrately, on the aim of clear displaying.

Below is the same quantity obtained utilizing real data.[11]

FIGURES

01.01.199601.01.199801.01.200001.01.200201.01.200401.01.2006

2000

4000

6000

8000

10000

12000DJIA current (5th ) EPOCH

χt (day)

Figure 1

Figure 2. a. and b.

皮下脂肪瘤介绍及治疗方法

【精编】皮下脂肪瘤介绍及治疗方法（含民间偏方） 1 皮下脂肪瘤皮下脂肪瘤在中医称为痰核。“肉瘤”之名出《干金要方》。多因郁滞伤脾，痰气凝结所致。以皮下肉中生肿块，大如桃、拳，按之稍软，无痛为主要表现的瘤病类疾病。最常见的好发部位为颈，肩，背，臀和乳房是起源于脂肪组织的良性肿瘤，由成熟的脂肪组织所构成。 1 疾病简介皮下脂肪瘤（lipoma）是脂肪组织的良性肿瘤。由成熟的脂肪组织所构成，凡体内有脂肪存在的部位均可发生。脂肪瘤有一层薄的纤维内膜，内有很多纤维索，纵横形成很多间隔，最常见于颈、肩、背、臀和乳房及肢体的皮下组织，面部、头皮、阴囊和阴唇，其次为腹膜后及胃肠壁等处；极少数可出现于原来无脂肪组织的部位。如果肿瘤中纤维组织所占比例较多，则称纤维脂肪瘤。 2 疾病分类根据脂肪瘤的可数目可分为有孤立性脂肪瘤及多发性脂肪瘤二类。此类肿瘤好发于肩、背、臀部、四肢、腰、腹部皮下及大腿内侧，头部发病也常见。位于皮下组织内的脂肪瘤大小不一，大多呈扁圆形或分叶，分界清楚；边界分不清者要提防恶性脂肪瘤的可能。单个称为孤立行型脂肪瘤。两个或两个以上的称为多发性脂肪瘤。

按部位不同可分为皮下脂肪瘤和血管平滑肌脂肪瘤（又称错钩瘤）。根据脂肪瘤发生的部位皮下脂肪瘤为扁平或分叶状、质软，边界清楚的皮下限局性肿物。质软，可推动，表面皮肤正常，发展慢，数目多达数百个，常在皮下。血管平滑肌脂肪瘤错钩瘤多发生于各个器官（肾脏，肝脏较为多见）的毛细血管的平滑肌组织之间的脂肪瘤（又称肾错构瘤，肝错钩瘤）。 3 发病原因皮下脂肪瘤指“脂肪瘤致瘤因子”在患者体细胞内也存在一种致瘤因子，在正常情况下，这种致瘤因子处于一种失活状态（无活性状态），皮下脂肪瘤正常情况下是不会发病，但在各种内外环境的诱因影响作用下，这种脂肪瘤致瘤因子的活性处于活跃状态具有一定的活性，在机体抵抗力下降时，机体内的淋巴细胞、单核吞噬细胞等免疫细胞对致瘤因子的监控能力下降，再加上体内的内环境改变，慢性炎症的刺激、全身脂肪代谢异常的诱因条件下，脂肪瘤致瘤因子活性进一步增强与机体的正常细胞中某些基因片断结合，形成基因异常突变，使正常的脂肪细胞与周围的组织细胞发生一种异常增生现象，导致脂肪组织沉积有关，并向体表或各个内脏器官突出的肿块，称之脂肪瘤。[1] 4 发病机制皮下脂肪瘤是相当常见的皮肤病灶，由正常脂肪细胞集积而成，占软组织良性肿瘤的 80%左右，无明显特殊病因，常发于皮

完整版皮下脂肪瘤介绍及治疗方法含民间偏方

精编】皮下脂肪瘤介绍及治疗方法（含民间偏方） 1皮下脂肪瘤皮下脂肪瘤在中医称为痰核。“肉瘤”之名出《干金要方》。多因郁滞伤脾，痰气凝结所致。以皮下肉中生肿块，大如桃、拳，按之稍软，无痛为主要表现的瘤病类疾病。最常见的好发部位为颈，肩，背，臀和乳房是起源于脂肪组织的良性肿瘤，由成熟的脂肪组织所构成。 1 疾病简介皮下脂肪瘤（lipoma ）是脂肪组织的良性肿瘤。由成熟的脂肪组织所构成，凡体内有脂肪存在的部位均可发生。脂肪瘤有一层薄的纤维内膜，内有很多纤维索，纵横形成很多间隔，最常见于颈、肩、背、臀和乳房及肢体的皮下组织，面部、头皮、阴囊和阴唇，其次为腹膜后及胃肠壁等处；极少数可出现于原来无脂肪组织的部位。如果肿瘤中纤维组织所占比例较多，则称纤维脂肪瘤。 2疾病分类根据脂肪瘤的可数目可分为有孤立性脂肪瘤及多发性脂肪瘤二类。此类肿瘤好发于肩、背、臀部、四肢、腰、腹部皮下及大腿内侧，头部发病也常见。位于皮下组织内的脂肪瘤大小不一，大多呈扁圆形或分叶， 分界清楚；边界分不清者要提防恶性脂肪瘤的可能。单个称为孤立行型脂肪瘤。两个或两个以上的称为多发性脂肪瘤。 按部位不同可分为皮下脂肪瘤和血管平滑肌脂肪瘤（又称错钩瘤）。 根据脂肪瘤发生的部位皮下脂肪瘤为扁平或分叶状、质软，边界清楚的皮下限局性肿物。质软，可推动，表面皮肤正常，发展慢，数目多达数百个， 常在皮下。血管平滑肌脂肪瘤错钩瘤多发生于各个器官（肾脏，肝脏较为多见）的毛细血管的平滑肌组织之间的脂肪瘤 又称肾错构瘤，肝错钩瘤）。 3发病原因皮下脂肪瘤指“脂肪瘤致瘤因子”在患者体细胞内也存在一种致瘤因子，在正常情况下，这种致瘤因子处于一种失活状态 无活性状态），皮下脂肪瘤正常情况下是不会发病，但在各种内外环境的诱因影响作用下，这种脂肪瘤致瘤因子的活性处于活跃状态具有一定的活性，在机体抵抗力下降时，机体内的淋巴细胞、单核吞噬细胞等免疫细胞对致瘤因子的监控能力下降，再加上体内的内环境改变，慢性炎症的刺激、全身脂肪代谢异常的诱因条件下，脂肪瘤致瘤因子活性进一步增强与机体的正常细胞中某些基因片断结合，形成基因异常突变，使正常的脂肪细胞与周围的组织细胞发生一种异常增生现象，导致脂肪组织沉积有关，并向体表或各个内脏器官突出的肿块，称之脂肪瘤。[1] 4发病机制皮下脂肪瘤是相当常见的皮肤病灶，由正常脂肪细胞集积而

眼角长了个小疙瘩怎么办

如对您有帮助，可购买打赏，谢谢 眼角长了个小疙瘩怎么办 导语：眼睛长了个小疙瘩是很常见的现象，在这样的情况之下，就好好的进行观察，自己的小疙瘩是什么样的，然后及时的去医院做检查，及时的检查，及 眼睛长了个小疙瘩是很常见的现象，在这样的情况之下，就好好的进行观察，自己的小疙瘩是什么样的，然后及时的去医院做检查，及时的检查，及时的治疗，这是非常不错的，这样就会更好的让自己的身体恢复健康，这样是非常的不错的，那就好好的进行治疗就好了。 应该是麦粒肿的症状，别担心，初起有眼睑痒、痛、胀等不适感觉，之后以疼痛为主，少数病例能自行消退，大多数患者逐渐加重。检查见患处皮肤红肿，触摸有绿豆至黄豆大小结节，并有压痛。如果病变发生在近外眼角处，肿胀和疼痛更加明显，并伴有附近球结膜水肿。部分患者在炎症高峰时伴有恶寒发热、头痛等症状。外麦粒肿3～5日后在皮肤面，内麦粒肿2～3日后在结膜面破溃流脓，炎症随即消退。也有部分麦粒肿既不消散，也不化脓破溃，硬结节长期遗留者。它是一种没有明显疼痛的表面皮肤隆起，主要是眼睑腺体阻塞造成的伴有炎症的话才会自觉的疼痛的症状。小的霰粒肿可以热敷或者理疗按摩疗法，促进消散吸收，较大大的或长时间不能吸收的可以择期手术治疗. 这是脂肪粒，等长时间长了，熟了自己挤就行。先说说脂肪粒的产生（从其他地方转来D，自己还没那么厉害，呵呵 1、体内原因：眼部、面部出现油脂粒大多是由于近期身体内分泌有些失调，致使面部油脂分泌过剩，再加上皮肤没有得到彻底清洁干净，导致毛孔阻塞，很快形成脂肪粒。2、外在因素：眼睛周围是全身最薄的皮肤，约0.07毫米，又没有皮下腺，加上人眼一天频繁眨动，特别容易缺水、干燥、 预防疾病常识分享，对您有帮助可购买打赏

皮下组织有疙瘩是怎么回事

皮下组织有疙瘩是怎么回事 在一般的情况下，大家对身体健康和皮肤护理都特别的主要，尤其是在夏天的时候，皮肤都暴露在外面，接收来自外界的各种刺激，在这样的时候更要做好对皮肤的护理。有时候我，我们会发现在皮肤的下面长出来好多的小疙瘩，这样时候就会让我们感觉到不知道是怎么回事也不知道要怎么治疗。 ★考虑是毛周角化症 毛周角化症俗称“鸡皮肤”，是一种先天遗传病，个人症状 有轻有重。身体缺乏维生素A皮肤干燥，或者天气较为干燥寒冷，毛口收缩的时候腿上汗毛长不出来，症状较明显，夏季则症状较轻。一般不痛不痒，过度清洁时也可能出现瘙痒情况。 ★对策： 毛孔角化症属于先天遗传病，并不能根治，只能通过利用A

酸，或含果酸、乳酸等成分的产品保养皮肤，改善皮肤的角化程度。可去药店咨询医生购买水杨酸类软膏。 ★缺乏维生素A加重小红疙瘩 皮肤下面有小红疙瘩除了与天生体质有关以外，缺乏维生素A引起全身性的皮肤干燥也是加重症状的原因之一。 ★对策 1、洗澡不要用太热的水。过热的水会让皮肤上的皮脂过分流失，这样会加重皮肤干燥。 2、洗澡后抹身体乳。保证皮肤水分充足能有效减轻腿上小红疙瘩，所以可以在每次洗澡后涂上身体乳液。

★可能是闭头粉刺 如果是额头、下巴等部位皮肤下有疙瘩，刚开始是黄白色，不痛不痒，天气炎热脸上油脂分泌旺盛时会有发红，多是闭头粉刺。 ★对策 1、及时清洁皮肤，注意补水，不要使用刺激性护肤品，不要用过于油腻滋润的面霜。 2、多运动促进皮肤排汗，使毛孔中的油脂脏污随着汗水排出，防止油脂堵塞毛孔发炎。 3、多喝水、多吃蔬果，饮食清淡。

4、必要时看医生。 ★可能是脂肪粒 如果皮下的疙瘩是乳白色的，不痛不痒，不受天气、温度等影响，用手不容易挤出，且多分布在眼角周围，考虑是脂肪粒。 ★对策 1、脂肪粒多是皮肤营养过剩引起的，建议不要使用太油腻的护肤品。 2、可取美容院用针挑破，挤出脂肪粒。(别用手挤，小心皮肤感染发炎)